just because here are a lot of people new to crypto, I want to share my thoughts. Online wallets are dangerous and defeat the purpose of a blockchain, because theire centralized...
No one forces us to use the online wallet offered on my.electroneum.com. It is there for new people entering the crypto world. Electroneum strives to enter the mass market (with mobile "mining") and those new users need a simple interface to manage their coins. No one would expect them to understand how coins are stored on a printed piece of paper, or how to use the command line interface and sync the node with the ETN blockchain.
Those who are experienced are free to use the offline (paper) wallet, along with electroneumd and electroneum-wallet-cli. The keyword here is "choice".