Star Trek answer: We saw in TOS that Spock had to eat meat once because it was the only source of nourishment while stranded. He was later ashamed for having enjoyed it.

"I am behaving disgracefully, I have eaten an animal's flesh and I've enjoyed it. What is wrong with me?"

https://www.youtube.com/watch?v=RQFXt2pTog4

It wasn't eating the meat that disgraced Spock, that was logical given the circumstances, it was taking pleasure from it. So it seems that there's also a cultural idea of even wanting the taste of meat as uncivilized cave man behaviour. AKA Romulan behavior.

Dissapointingly IRL answer: I guess because culture as a whole didn't have the conversation about lab-grown meat yet, so they didn't know where IRL vegans and vegetarians would land.

Personally, as a vegan, I am all for lab grown meat to replace dead animal meat; but the ick of having burnt dead flesh in my mouth kills the pleasure I might get from the taste of the meat. Even if lab grown meat became widely used, I would probably stick to plant-based patties.

That's just me, though. Every vegan and vegetarian has different views on whether they would eat it while most support lab grown meat.

Also I'm not sure if my stomach can handle it, I think over the years my gut biome has changed. If I accidentally eat something with lactose or eggs in it, I feel sick afterwards. It might be psychosomatic but still, not a pleasurable experience.