Here you can find the whole guide. It's a simple procedure. https://medium.com/eidoo/how-to-backup-eidoo-private-keys-ce2a7ebdae7f
Even if it is easy in the future Eidoo should provide the option to make the seed or backup phrase like they are calling it to work with different wallets. Take some bitcoin wallets that let you recover even if you lose the wallet, a good example is the Ledger wallet which is a hardware one but you can recover it with the backup phrase in Electrum or Mycellium as long as both wallets have the same BIP compatibility. That is what Eidoo should do and why not to make a desktop wallet since many Ethereum desktop wallets are not secure.
Yeah, who's to say I should be trusting this random company with my ETH which is conveniently at an ATH like the rest of the cryptocurrency marketplace right now. They SHOULD give people the ability to get their coins in the off chance that they ever go under, it's pretty much like BitGo does it where they allow you to get your coins if they were to go under.
And companies go under all the time in Cryptocurrency, especially ones that are online wallets