Are PSUs something I should "upgrade" with time even if I don't need the extra power?
I've been using a Corsair TX750 since my i5-750 days, and never had a PSU-related issue. I'm now running a 2500k with a 970, and am planning to upgrade before September to a Ryzen 5 or 7 (either the current 2000 ones or the new 3000 - depends on the pricing here in Brazil), and maybe a new GPU (didn't really decide which one, but nothing too fancy as I'm still going with 1080p).
Should I start looking for PSUs as well? A modular one feels is tempting for cable management, but I'd rather spend the money somewhere else.
A lot of people undervalue the importance of a quality power supply. Keep in mind this is the sole component that provides electricity to your entire system. Also in the inverse a cheap power supply can lead to potentially catastrophic failure.
A failed video card or ram cannot take out the rest of your equipment. A failed PSU however can kill your motherboard, ram, gpu, and anything else plugged into.
Highly rated power supplies typically are built to last (check out anything manufactured by SeaSonic or Superflower for quality units). A good quality PSU can last for many years, but like all things they eventually deteriorate and the capacitors on them can fail after prolonged use.
Your Corsair TX750 is a Seasonic manufactured unit if you aren't aware. I typically don't keep a PSU any longer than 5 years. 7 years is pushing it a bit. I would definitely consider looking into a replacement rather than the alternative of just waiting for it die on it's own and the potential ramifications that entails.