In general, we are assuming that tags are correct. In most cases, the user tags their question with mostly appropriate tags. Even if the question has been migrated, the tags are still appropriate to be there.
The tags are there so that anyone searching might come across that question. If they have a similar question it would be helpful to know that the first one was migrated as 'does not belong here'. So it still needs to be searchable.
The tags should not be editable because, once migrated, the question should not be changed in any way, otherwise it opens up the possibility of having migrated questions that are fundamentally different.
I'm in favour of keeping it the way it is.
Although, moderators should be able to update 'outdated/deprecated' tags on closed questions.