Just to supplement your point with an anecdote: my first "proper" Jellyfin host was a retired Optiplex 3020. I added a 128GB SSD through one of those silly CD drive bay adapters and threw in a Quadro P400 that I bought off of eBay. On top of that, the actual server ran Proxmox with Jellyfin nested in an LXC container. By all accounts, the machine was a janky pile of e-waste given a new, horrible life through sheer stinginess.

There were quirks (mostly self-imposed ones) to getting the whole thing set up, but it ran like a champ for the better part of a year. Hardware transcoding really does make a world of difference, even in the worst of cases.