BTW, do you know your coins' history? You do know that ISIS coins might be sitting on your wallet right now, right?
Because, you know, when you buy a house, the state knows who you are, it's not an anonymous transaction for some weed, so prepare yourself for some trouble if even a single satoshi is deemed "tainted"...

It stops being peer-to-peer cash if you deposit it in a CEX. Their platform, their rules. If they discriminate based on inaccurate bullshit, then I'd never use them, especially for such large amount. If you want instant liquidation, then you'll probably have to weigh the tradeoffs.
You'd never use them, but the guy who sold you the house most likely would.
And in that case, the police would knock your door... you'd have some explaining to do.
I know people who bought their first house with Bitcoin. Due to ridiculous rent prices (it's not just Airbnb) it makes sense for someone to buy a house if he can afford it.