Drawbacks of close source?
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You don't know what's happening behind the scenes and what the developers are doing. I'm not saying Exodus is doing that, but you can't know for sure that the team is not saving your seedphrase, or private keys without your knowledge, or if there's is backdoor.

An example of something similar happening is Atomic wallet. Multiple user's wallets have been hacked recently when the wallet claimed to be "non-custodial", how could this have happened when there is no centralized server that holds the private keys like it is the case with exchanges?