Many PSUs do have bleed resistors, but plenty (especially cheaper ones) will not. More importantly, a damaged PSU may have a non-working bleeder circuit, and you'll only know when you discharge a cap. Hopefully across a resistor, rather than a screwdriver, and very much hopefully not an open wound on your skin.

A CRT stores energy because it acts a a large capacitor. Some better monitors (especially late '90s open cage arcade monitors) had bleed resistors on the anode of the CRT to make servicing safer. It's not actually a ton of energy; the voltage is very high, but that's about it. A charged, unpowered tube will sting, but it's seldom a killer. The flyback transformer will give a potentially lethal shock, though. The anode cap has the thick insulation and is surrounded by aduadag for a reason!