To be honest you probably won't save money as you'll be more likely to upgrade regularly. I bought my Framework 13-inch last year and already bought a gorgeous new matte screen for it, and I'd been eyeing upgrading the mainboard with the new AMD one now. In the past with laptops I'd hold onto them for years until they couldn't perform, and now I'm considering upgrading my device a second time within only a year?
I really do love my Framework, but the easier upgradability makes upgrading more likely, which means more expenses - unless you can restrain from upgrading more often than you would on a laptop. Since budget seems to be a concern for you this may be worth keeping in mind. On the other hand though, I'd be concerned about how long a $500 laptop will last you anyway (the ones I used for years were more like $1200).
One final thing - some parts can't necessarily be carried over when upgrading to a new generation. For example, to upgrade to the AMD mainboard I'll also have to buy new RAM as the generation upgraded to a newer variant. If I want to use my old mainboard as a home server, I'll also have to purchase replacement parts for what it loses in the upgrade (new hard drive, new expansion ports, cheap case). It's great if you had an existing need for a home server, not so much if you didn't. Since I hate throwing out electronics I'll end up buying more to keep it operational, even though in practice I won't use it very much.
TL;dr - Framework makes upgrading and reuse cheaper and easier, which if you're like me makes you spend more money and upgrade more frequently.