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I think what would solve the problem is if the exchanges themselves offered a 3rd party website with all the wallets. I mean, they already have 90% of them built into their exchange. But I suppose they have no motivation to do that.

Coinomi supports over 100 coins and tokens including ETH, BTC, ZEC, LTC, etc.

They are working on support for Monero

Scroll down for supported coins

https://coinomi.com/