Annotated tags can be signed and you can check tag signatures in addition to commit hashes. Admittedly, if you don't trust the remote repo you don't trust the remote repo even with signatures.
Similarly, many repository hosts can help you setup tag protection as a part of branch protection tools, but while that helps with your own repos it doesn't generally help with remote repos.
Checking signatures will tell you that X created tag Y, but tells you nothing about "Y has not changed", regardless of how Y has changed. But yeah, I wish more setups would sign things.
And agreed, tag protection rules do exist and are fairly common. Though by far the majority I run across do not protect tags or branches by default. And even if they do, external systems may or may not honor changes - that's why dependency management lock-files exist, to detect changes like this where the "name" (i.e. tagged version) stayed the same but the content changed.
Or in a different flavor, you have Go modules, where you cannot ever remove or mutate a tagged version in the main proxy... but you can change it in github, and now your web-UI-visible code differs from what people download. Which may be worse, because while go.sum will store the go module checksums and can complain if you pull the wrong contents, that checksum doesn't match the sha it pulled. If you have a module-compatible tagged version, the git sha isn't stored anywhere, you just have `require thing v1.2.3` and the go module content hashes. Trying to "recover" the sha from this can be rather painful, as you essentially have to check the module checksum for all shas in a repo... assuming it even still exists.
Yeah, at the end of the day it is all about trust. If you trust that X creates tags that don't change, that signature is a trust document.
Right, as with many things in computing often you want "trust, but verify". Trust a good tag by a good author not to change, but also go ahead and store a hash in a lockfile and verify it, just in case.
Similarly, many repository hosts can help you setup tag protection as a part of branch protection tools, but while that helps with your own repos it doesn't generally help with remote repos.