I installed Electrum and created a wallet there. All I know is the seed generated. I don't know private keys from the Bitcoin addresses it manages for me. And I don't see an option to get them from there. So, the question is how safe this system is? Won't I lose my bitcoins one day?
Tools -> View Addresses -> Right-click an address -> Private Key; done. You have it.
And why would you lose your Bitcoins one day simply because your wallet is "managing" them for you? The seed is - in simple words - just a key that tells the software which addresses to generate for you (so it can regenerate them anytime if you need to restore your wallet).