Are there any exchanges, that matter, left that doesn't support Segwit?
I think there are a few services that are quite popular, but they still not support SegWit. I read that
Binance is one of them, but also very popular blockchain.com and BitPay. Maybe they do not care too much for their users, or they like to take more fees when they withdraw, but they can set fixed withdraw fees even with SegWit.
If I remember correctly the Legacy wallet address is compatible with all types since it can send and receive to all types of bitcoin address. But Native Segwit and Nested Segwit have limited compatibility I guess they can only send and receive from legacy but not from each other.
You can send from any type of Bitcoin address to another address from your personal wallet, there is no problem with that. Problem is in fact that some services/exchanges still not supporting native SegWit (bc1), so if you use such address in your wallet and try to withdraw from exchange that not support it, only way around is to switch to nested SwgWit (address starting with 3) or to use Legacy type address.