The private key is a very long letter/number. But do most people write that down as well?
Just that seed phrase are easy to write down. Private key was created in non deterministic wallets even before seed phrase creation, it was backup at the time, but I can not recommend writing down private key. As seed phrase was invested, I can not be comfortable to backup private key, I would prefer seed phrase as it is easy to backup with just 12 to 24 words.
you could always extract it from your seed phrase using iancoleman's BIP39 tool.
Yes, but only for BIP39 seed phrase. Like Electrum seed phrase, Iancoleman can not be used to generate Electrum wallet private key from its seed phrase because the way the seed phrase are generated are not the same.
What if you only have the private key but not the seed phrase?
If you have the private key to your coin, you can use it to recover your coin and spend from the coins.