That would be hilarious. Mr Adventure as a bored museum security guard, ripe for defeat in his red shirt...... the whole scheme to steal the ship would have been different, and comedic, and awesomely 80s.
Enterprise as a museum piece would be interesting, but might be seen the wrong way. Especially if they did make a 1701-A in 1979 and left the original 1701 as a lifesize museum where the crew would have to remove the velvet ropes and all as well as fetch compatible lithium and so on. That'd almost be a movie in of itself. Plus, TMP did establish it's the same ship but a major refit

As for comedy, it's the other way around for me. Comedy is the cancer that killed the franchise, especially during the 1990s.
STIV had it and was a hit given its forcing the crew into modern day Earth. "Fish out of water" works. Some humor has dated but the story is still more or less watchable. But it started the trend...
The rot really starts when the demand for comedy was rolled into STV, where the fish out of water trope no longer begins to hold up (much less be applied because they're back in their proverbial stream) and the crewmembers are used as joke fodder and little more. At least Kirk was used as the butt of jokes as well, it'd be worse if he hadn't. Note that STV's best scenes are played out utterly seriously too... The comedy sticks around and hampers STVI, with Uhura getting by far the worst treatment.
TNG time: People laugh at "Oh ****!" in that comedynonfest of VII only because it's a shock, not because it's actually thoughtful comedy. Do I need to mention Captain Stewart Wimpy's "by Tuesday" routine, which was played out even before the first instance was uttered? VIII falls flat with its comedy despite edging back into "fish out of water" but making the mistake of mixing comedy with a more dire and palpable situation than "The whales, what if". But the plot is so cliche and it's the direction, not the pee joke and title reference joke that keep the movie afloat. IX holds back on the comedy, but the problem is the script is laughable and I've not mentioned that stupid singalong yet. With X they all finally realize the comedy act diluted the series' credibility. But there's too much in that script that's even more laughably bad and even the horror and grim aspects feels a bit forced. Then there's the bottomless pit, which must have been the worst joke of them all...
Then come the Dyn-o-mite JJ Kelvin reboots, which are more throwaway comedyfests, using superficial stereotype traits and generally lacking the sort of depth that good Trek is known for...
But some people like comedy. Others, not so much. For me, anyway, the occasional joke that flows with the plot and not aimed at or hinted at or nudged/winked to the audience (e.g. McCoy vs Spock a zillion times in TOS) just works best as, to me, it's the most tactful. YMMV... The debate will never end.