What is the biblical basis for saying that Matthew 22:30 refers to all marriages ceasing at death?

As with many questions about a given pericope, an answer is often found in another pericope. That's the analogy of Scripture. The best interpreter of Scripture is Scripture. Sometimes errors in interpretation creep in because interpreters do not consult relevant scriptures.

In this instance, the apostle Paul's words to the Ephesian Christians are particularly relevant.

Husbands, love your wives, just as Christ loved the church and gave himself up for her to make her holy, cleansing[b] her by the washing with water through the word, and to present her to himself as a radiant church, without stain or wrinkle or any other blemish, but holy and blameless. In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. After all, no one ever hated their own body, but they feed and care for their body, just as Christ does the church—for we are members of his body. “For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.”[c] This is a profound mystery—but I am talking about Christ and the church. However, each one of you also must love his wife as he loves himself, and the wife must respect her husband 5:25-33 NIV).

The only marriage that will exist in heaven is the marriage of the church universal, the bride, to her Lord and Savior, Jesus Christ, the bridegroom and head of the church. In heaven, Jesus will be the focus of attention of each and every believer.

That is not to say earthly marriage is unimportant or that couples who were married during their lifetime on earth will have no relationship with each other in heaven. I see nothing unbiblical about the belief that all believers will recognize and enjoy fellowship with each and every person they knew prior to the resurrection. Moreover, they will likely get to know in heaven many, many other fellow believers, and they will join with them in praising God for all eternity.

After all, Jesus's inner circle of Peter, James, and John recognized Moses and Elijah at Jesus's transfiguration (Matthew 17 and Mark 9). Impetuous Peter, immediately upon seeing Jesus speaking with Moses and Elijah, became almost tongue-tied out of fear from what he was seeing. He did, however, manage to suggest that they all set up camp there on the mountain. Though perhaps well meaning, Peter did not grasp the unique and singular nature of Jesus's personhood. For that reason, we read further in Mark's account of the transfiguration,

Then a cloud appeared and covered them, and a voice came from the cloud: “This is my Son, whom I love. Listen to him!”

Suddenly, when they looked around, they no longer saw anyone with them except Jesus (my bolding).

In conclusion, in the resurrection all believers will see Jesus in a way they never could during their time on earth. Until then, the apostle Paul reminds us that on this side of eternity, as with the other side of eternity, our focus should be on him only and on his words. Why? Because

. . . [H]e is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence (Colossians 1:18).

The supposition that earthly marriage somehow survives the threshold of earthly death stems from a misapprehension of just what Christ has done and just how we may be united with Him.

Know ye not, brethren, (for I speak to them that know the law,) how that the law hath dominion over a man as long as he liveth? For the woman which hath an husband is bound by the law to her husband so long as he liveth; but if the husband be dead, she is loosed from the law of her husband. So then if, while her husband liveth, she be married to another man, she shall be called an adulteress: but if her husband be dead, she is free from that law; so that she is no adulteress, though she be married to another man. Wherefore, my brethren, ye also are become dead to the law by the body of Christ; that ye should be married to another, even to him who is raised from the dead, that we should bring forth fruit unto God.- Romans 7:1-4

In explaining the mechanism by which those who are in Christ are freed from the Law, Paul uses earthly marriage in exemplary fashion. Bodily death serves as the lawful nullification of the marriage covenant. If this were not so every widow and widower, in re-marriage, would commit adultery but now, through death, they are free.

The larger point Paul makes is that, in similar fashion, union with Christ involves union with His death. This union with Christ in His death and resurrection functions in the same way as with earthly marriage in the example given:

Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection: Knowing this, that our old man is crucified with him, that the body of sin might be destroyed, that henceforth we should not serve sin. For he that is dead is freed from sin. - Romans 6:3-7

As long as one's "old man" remains "alive" there is no lawful freedom to unite with Christ. In trying to make this truth evident, Paul points out that earthly marriage is an excellent example of this; that so long as one spouse is alive there is no freedom to marry another.

If it were not actually true that death dissolves earthly marriage Paul's point cannot stand as he would have used a false statement to buttress his argument. It was in this that the Sadducee's ultimately greatly erred: That they did not recognize, in the typology of the covenant of marriage, the greater truth of Messiah ending the old in order to bring in the new.

Then came to him the disciples of John, saying, Why do we and the Pharisees fast oft, but thy disciples fast not? And Jesus said unto them, Can the children of the bridechamber mourn, as long as the bridegroom is with them? but the days will come, when the bridegroom shall be taken from them, and then shall they fast. No man putteth a piece of new cloth unto an old garment, for that which is put in to fill it up taketh from the garment, and the rent is made worse. Neither do men put new wine into old bottles: else the bottles break, and the wine runneth out, and the bottles perish: but they put new wine into new bottles, and both are preserved. - Matthew 9:14-17

Let's get that full context and it should become more apparent.

23 The same day came to him the Sadducees, which say that there is no resurrection, and asked him, 24 Saying, Master, Moses said, If a man die, having no children, his brother shall marry his wife, and raise up seed unto his brother. 25 Now there were with us seven brethren: and the first, when he had married a wife, deceased, and, having no issue, left his wife unto his brother: 26 Likewise the second also, and the third, unto the seventh. 27 And last of all the woman died also. 28 Therefore in the resurrection whose wife shall she be of the seven? for they all had her. 29 Jesus answered and said unto them, Ye do err, not knowing the scriptures, nor the power of God. 30 For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.

So if people simply don't get married in heaven but stay married to their earthly spouses, then the lady in the Sadducees' story is married to seven husbands. In that case Jesus' answer doesn't make sense: the Sadducees raise an objection (that resurrection implies polyandry in heaven), and he says "Ye do err" and then tells them they're essentially right, that the lady's still married? Not reasonable. He instead says the resurrected are "like the angels" and therefore it's not a problem. If it's not a problem, the lady didn't stay married to 7 husbands in heaven.

This is repeated definitively by St. Paul in Romans 7:2-3:

By law a married woman is bound to her husband as long as he is alive, but if her husband dies, she is released from the law that binds her to him. So then, if she has sexual relations with another man while her husband is still alive, she is called an adulteress. But if her husband dies, she is released from that law and is not an adulteress if she marries another man.