Can I DCA without having a wallet at all?

There is always a lot of healthy discussion about the pros and cons of hardware vs software wallets, with clear preference for hardware wallets.

My question is, if you’re in a phase where you only ever add to your wallet, do you need a wallet at all?

Clearly you need one to start off, create a seed phrase and get an address, but after that couldn’t you clean up every scrap of evidence of that wallet app, keeping of course the address and seed phrase somewhere, and then just send to that address however you like?

Is that possible and even more secure than a hardware wallet?