Exodus wallet has a great reputation
No, it hasn't.
Actually, exodus is a pretty bad wallet with missing features (e.g. multi signature) and low security standards (i.e. seed exposed after unlocking the wallet).
The fact that it is closed source, doesn't make it any better.
There are lots of better wallets to choose from. I'd never recommend exodus to anyone.
it requires no verification and provides you with strong transfer speed and the ability to back up your assets
Uhm.. yes.. that's what you would expect from any wallet for a decentralized currency relying on cryptography?
Btw.. the "transfer speed" is not related to the wallet at all.