The main issue I see with that option is space and power, the micro-form factor (NUC-sized) clone systems that people are discussing in here are quite nice for that. Functionally an old Dell tower should be fine.
Sure, but those tend to be much more expensive, so depending on the actual cost of electricity in your area, it may take a long time for you to break even.
However, if you want to have a really small appliance-like pc, then yeah, the NUC-sized ones are much better.
The low-power AMD based systems everyone recommended a couple years ago were indeed great, until the ebay resellers realized what was going on and started slapping "opnsense pfsense AES-NI" etc on their listings and doubled their prices. The systems went from selling at $40-50 to over $100.
Also, the AMD processor in those systems is getting extremely long in the tooth.
However, if you want to have a really small appliance-like pc, then yeah, the NUC-sized ones are much better.