Why does everyone talk about wallets like they're a given?

I never got interested in wallets because I'm just holding now: I just buy BTC in an exchange, and send it to a public address that I generated from a seed (offline), in a computer that'll never be online.

That being said, I feel like everyone talks about wallets like they're almost an integral part of BTC, when in reality wallets are nowhere to be mentionned in the Whitepaper, and Satoshi himself never talked about wallets. I feel Bitcoin is supposed to be trustless but I feel like everyone feels fine with a third party software that they don't really know how it works (see what happened lately with Ledger...)

So is there something I'm missing? Isn't there some way to transact BTC without a wallet?

Edit: I understand the benefits of having a wallet, the generation/management of keys, etc. I'm just aware that all that was built on top of BTC, and was just wondering what was the original, raw way to send BTC, without a wallet.