Why don't Reformed Christians consider it necessary to confess to a priest?

I think Reformed Christians believe that salvation is a one and done event accomplished by Christ without intervention by man.

If one believes that you are once saved always saved, then nothing you can do, confessing or being an atheistic mass murderer can unsave you.

My personal opinion is that this cannot be supported by either scripture or the traditions of the apostolic churches.

But this is what they believe. Im eastern catholic and I do believe that the apostles were clearly given authority to administer ministries to bind and lose in the Church.

Disclaimer: I am not a pastor or trained theologian.

(Other disclaimer: Since your question asked about a Protestant perspective, this answer is written from that perspective with respect to various claims made. Feel free to mentally sprinkle "according to Protestants" in front of everything.)

That said... your main question appears to be about private confession, but you also mentioned penance, so I will address both.

Private Confession

My guess is that requiring private confession would be seen as a form of works righteousness. "For by grace you have been saved [...] not a result of works" (Ephesians 2:8-9). Salvation is the free gift of God; there is no act we can do as humans to "merit" salvation, and so saying that anything, besides wad Christ has already accomplished, is necessary for salvation would be considered by many Protestants to be heretical. (For more information, see what your Protestant/Reformed denomination of choice has to say about "sola gratia" / "grace alone". I'll omit links because Wikipedia's article is unhelpful, and for anything else I'd likely have to cite a source from a specific denomination.)

(I won't go into the rabbit hole of whether repentance is "necessary". On the one hand, it is. On the other, we are incapable of repenting on our own, and it is only through the Spirit working within us that we can repent. However, there is no specific mechanism of repentance required.)

That said, there are means by which God's grace is made manifest... one of which is confession. At least some Protestants commend parishioners to engage in private confession, as there are significant benefits (for one, the relief of conscience to be had from receiving forgiveness one-on-one after confessing specific sins). However, it is not required.

Penance

Protestants, AFAIK (Evangelicals/Lutherans, certainly) mostly reject penance, for much the same reason; it leans very much to being a form of works righteousness. No act we can do as humans can make up for our Sin; only Christ's death can accomplish that. And since Christ already died for us, and His redemption is complete (John 19:30), no act we can do can "add" to what He has already done.

That's not to say that some form of penance (and here I'm thinking more something that an individual chooses for themself, rather than something "assigned" by a priest) might not be salutary, but it must rightly be an act which is undertaken freely, and not because it is seen as "necessary" or as having some benefit with respect to our salvation.

Firstly, penance was rejected at the time of the reformation because the doctrine was based on a mistranslation of the Greek word metanoia - "repentance". The Latin Vulgate had, poenitenitam agite - "doing acts of penance". Martin Luther was the one who originally made this discovery.

Secondly, although James 5:16 says "confess your sins to each other", the New Testament does not contain anything to do with confessing to a priest or doing penance for confessed sins. Protestants believe that confession is something which is a good thing to do in the Christian community, individually and corporately, but it is not something which believers have to do to a priest. Which leads onto...

Thirdly, there is an important difference between Protestant understandings of priesthood and the sacraments. For example, Protestants would reject a pastor being a "priest" (because of the priesthood of all believers, e.g. 1 Peter 2:9 "you are a chosen people, a royal priesthood". In the Church of England, the word 'priest' was retained but only inasmuch as it is derived from a medieval contraction of the Greek word presbyter - elder). Protestants also believe in only two sacraments - the Lord's Supper and Baptism (e.g. 39 Articles, article XXV).

In sum, to answer the question properly you really have to explore the much bigger difference of priesthood in Catholic and Protestant understandings as well as the Sacraments, Scripture and Tradition. And, because repentance is such a big part of the Christian life, it goes even further back to what Catholics and Protestants believe about the Christian life (e.g. sanctification and justification). So it's no small question!