You definitely need to worry about safety. These wallets may give you control over your private keys but can you know for sure what are they are not storing the same keys on their servers? You don't because the wallet is not open source so It's not really suggested to use them for storing large amounts.
Do you have any proof on that? You should also be more specific which wallets are not open source and not lump all of them in one category.
I also believe being a staff member in the forum should make you choose your words more wisely. The newbies, the real ones, look up to you and some take your word as "truth" without debate.
What do you mean? Everything he said is true.
What kind of proof do you want? Don't you have Google?
Jaxx:
Jaxx is not open source, although the full code (minus UI) is visible on the website.
https://decentral.zendesk.com/hc/en-us/articles/217877528-Is-Jaxx-Open-Source-Exodus (and Eden):
Exodus is NOT 100% open source.
http://support.exodus.io/article/89-is-exodus-open-sourceCoinomi:
Coinomi (android wallet) is not opensource anymore and they havent pushed any source code updates for about a year now. Use with caution.
https://www.reddit.com/r/Bitcoin/comments/6rbzwm/just_noticed_coinomi_android_wallet_is_not/
Please link me one multi-coin wallet that is 100% open source.