Why do passports belong to a country and not to the citizen?

In Germany the administrative regulation detailing the application of the passport law, in German here, states:

1.4.2 Pass bleibt Eigentum der Bundesrepublik Deutschland
Der Pass bleibt auch nach Aushändigung an die antragstellende Person Eigentum der Bundesrepublik Deutschland. Daraus folgt nach allgemein anerkannten völkerrechtlichen Grundsätzen, dass andere Staaten über Pässe der Bundesrepublik Deutschland nicht verfügungsberechtigt sind. Dies gilt auch in umgekehrter Weise hinsichtlich der Nationalpässe anderer Staaten.

("The passport stays property of the Federal Republic of Germany even after being handed out. Consequently, according to the generally accepted principles of international law, other nations have no power of disposal over passports of the Federal Republic of Germany. This applies in turn equally to passports of other nations.")

I think this is the main rationale: A passport is of central importance to the welfare of its holder. In essence, it links an individual to their government which in turn is entitled and obliged to render support abroad. This link and authorization is protected by the authority of the German government by making the government, not the holder, the owner.

(Other reasons suggested, such as the right to revoke it or restrict its use, don’t seem compelling because government ownership is not a requirement for restrictions or revocations.)

Basically because no one may seriously testify to the worthiness of their own character or bona fides – in regard to travel as much as for anything else.

Passports – if you ever read them – say something like:

" . . . . The Minister of Foreign Affairs of Country requests all whom it may concern to allow the bearer, a citizen of Country to pass freely and without hindrance and to afford the bearer all necessary assistance and protection."

Even in the old days before international terrorism and all sorts of international crime, the word of a body appointed competent authority would be worth far far more than the word of a individual speaking on their own behalf.

Since the competent authority gives the undertaking on the passport, it is surely theirs to revoke if its terms are violated.

Hence it is their "property" but in the holder’s trust for safekeeping.

unlike driving licenses, national ID card

If you own something, you are able to sell it. Can you sell your driving license to another person? Can you sell your national ID card to another person? (Legally, anyway!) If the answer is no, then you don’t own it.

No country in the world allows this, so the premise of your question is fundamentally incorrect. Passports are issued by a country in the same way as all other formal documentation. At no point is any of this documentation a personal asset of yours.

Whether there is a mechanism for revoking or withdrawing any of that documentation would depend on the documentation and the country, of course. Driving licenses can often be revoked as punishment for unsafe driving. National identity cannot normally be revoked, although there are exceptional cases such as Shamima Begum. Regardless though, they are still not your property.

Because a country needs to be able to restrict what you do with a passport.

For example, they do not want you to be able to sell a passport, alter passport details, replace the photo with one of someone else, copy it, etc. While doing those things is often covered by fraud, you would usually have to be able to prove criminal intent. If the passport belongs to the state then they can make rules about what you can do with it, and not have anybody try to claim that "the passport is mine so I can do what I want with it".

It is more or less a legal detail to simplify a few procedures:

In most countries you are not necessarily entitled to be issued a passport. For example pending criminal charges or financial debt may be reasons good enough to refuse a person from being issued a passport to prevent the person from fleeing prosecution or debt collection. The same reasons can also cause already issued passports to be revoked and withdrawn with the requirement for the holder to return and surrender an already issued passport. This procedure is simplified if the issuing authority or state is the legal owner of the actual physical document. In some countries, the issuing state is also considered the legal owner of other documents, like e.g. driver licenses, as these can also be revoked and withdrawn.

Although not always honored, having the issuing state as legal owner of a passport also implicates according to international law, that foreign states are not allowed to seize or withdraw a passport without violating the property interests of the issuing state. In practice, it is however not particularly uncommon that foreign passports are seized in connection with for example refugee applications or forced removals and deportations.