While I can understand the dislike of wanting to see closed questions, my thought pattern is that the rather temporal nature of the "closed" status warrants the need of such an exclusive feature a bit moot. While the question is closed, usually views are wanted to either seal the fate of the question (deletion) or to save it (reopen).
I can see a bit of thought about the favorite tag highlighting on closed questions. I'm hesitant about it because there are always the scenarios where people do look for closed questions (we have a search term for it, even), and in that scenario, they may or may not find benefit in the visual filtering offered by the tag preference.
There's basically three routes that a closed question goes.
Question Gets Reopened
Either the closure was wrong in the first place, or there was improvement that helped repair the question into a proper state. Regardless of the reason that the question gets reopened, it remains that the question will need tags at this state. Removing the tags would require either someone needing to re-input the tags afterwards, or would require storing the tags silently.
Question is Duplicate, Stays Closed
Pretty much the only scenario a question should stay on the site after being closed, if it isn't simply awaiting reopening, is that it is a duplicate. Keeping around duplicates is helpful because it increases search results through the extra verbiage. To that end, visibility is still desirable, and removing tags would only serve to harm this visibility.
Questions shouldn't stick around closed except for this reason, generally. If it isn't something worth reopening, then the following should happen.
Question Gets Deleted
When it isn't a duplicate and it isn't salvageable, it's something that doesn't belong on the site. It's off-topic, it's a ranting discussion, it's not constructive, it's a survey, it's too vague or otherwise not a real question... all of these simply correspond to items you don't want people to find on the site - their fate is to get deleted. Even migration stubs do not need to stick around.
Deleted questions don't show up, period, so their tags do not interfere because it is as if it is not tagged.
The end result is, removing the tags for the closure duration is going to be summarily reversed, harmful, or of no effective impact. The time period during which a question should be closed, and the question does not deserve to have tags, should ideally be small. It may look like a big thorn during the early days, when traffic is slower, but once the site gets up to speed, it will be very unimpactful as long as diligence in maintenance is maintained.
It will take time for users to reach the required reputation level for community deletion, so until then, the moderators (pro tem moderator selections will come shortly after public beta starts) will have to assist in question deletion.
If you want to pay heed to keeping the site uncluttered, keep an eye on closed questions so that you can delete them in due time. Clean the site up and remove what is unwanted, don't leave undesirable junk lagging in dark corners, rotting and unwatched but still leading people to find the site for the wrong reasons.
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