-snip-Online wallet are the least you could use or get as a recommendation for use because they are not safe for your advantage, you will not have access to the private keys because they are connected to the internet and mostly are mobile wallets,
You've go it wrong here, online wallets are wallets that are connected to the internet, it doesn't mean you won't have access to your private keys, electrum is an online wallet, but you have access to your private keys when you use it.
Most of your comments are on point which deserved a merit, I'd just want to point out the correct terms here.
Electrum's default wallet types connect to the internet should be called "
Hot Wallet" instead of online wallet.
"
Online wallets" are mostly accessed though websites or even mobile apps connecting to it, the core difference is the wallet file is saved online into the wallet provider's server.
For example: Blockchain(
dot)com save their clients' "
wallet.aes.json" in their server while Electrum saved the wallet files locally in the user's PC.