Dude, in Power, Power Book II: Ghost, Empire, Succession, even in some K-dramas about wealthy people, they’re wearing designer stuff in every episode—even in their casual streetwear, hell, even their nightclothes! Is this unrealistic, or do rich people actually have ALL high-end designer clothes? Do some have shirts from Walmart or something?
With as much detail as you require, i.e. what they wear in bed at night, this question is nearly impossible to answer. As there is not a single person alive that has observed all rich people while they’re catching some zzz’s. It also hinges on the definition of rich.
Logically, the answer to your question is probably no. There will be a few rich people who wear non-designer clothes. But in my estimation they will be a minority. If you have the means, the show-off appeal or the perceived higher quality of the more expensive stuff is probably enough to fill your wardrobe over time. Also, rich people get a lot of shit for free.