In the case of coinbase, they require the user's phone number and I find that bizarre considering the purpose of a crypto wallet. I'll try blockchain it's been around since the beginning.
It has been around since the beginning but that doesn't make it safe to use. I would just go with a hardware wallet if I were you, you can store all cryptocurrencies, and you don't have to worry about the safety of your funds. If you don't have a budget for that (around ~100$) then Electrum for PC and Mycelium for android if using BTC. For other cryptos, you've got Trustwallet but it's not available for desktop.