In theory the C64 could experience bad caps, but it’s a much rarer of an occurrence than found in some Amiga models.
Ray Carlsen (Seattle, WA), the well-known electronics technician who builds his own high-quality power supply replacements for Commodore systems, had this to say to a forum member mrr19121970 on Lemon via an email exchange:
What does kill C64 machines (and some Amigas) are those old power-supply bricks. And when those components fail, they can shoot an over-voltage into the C64 and fry it beyond repair. This is one of the key reasons Carlsen creates brand new power supplies that are intended to last another 30 years or beyond, for both C64s and Amigas that rely on power bricks. I have several connections who have opted for the Carlsen-made PSUs, and they love them. I will likely be picking up some for my A500 and A1200 later this Spring. My C64 drives use bricks, too, which need to be modernized. Carlsen has affordable replacement solutions for those, too.I don't know where the "replace all caps" idea came from... perhaps from Amiga and Apple motherboards which have caps that do fail often and leak onto the boards. Commodore 8 bit stuff never needs routine cap replacement. I've never had to do that for a repair.
However, another option to consider for the C64 computer itself is the SAV64.
It allows you to use your existing C64 brick, but should the brick fail the SAV64 protects your machine (think of it as a fancy surge protector on steroids). It has an LED light to indicate the health status of your brick, which can be reset if need be. In addition to this barrier of safety, it also has power cord ports for 5VDC and 9VAC barrel connectors to allow easy use of alternative power sources - thus replacing your brick PSU altogether if you so desire. It is designed to handle 3 Amps in order to protect and power your C64 system.
I got a SAV64 this week.
Right off the bat, I noticed the the build quality is at a very high, professional level. This device was made to last and is like a little tank. The SAV64 isn’t a 100% guarantee of protecting the C64 against everything that could go wrong, but it’s a very reasonable insurance policy against one of the largest threats C64s face - the aging C= power bricks. There are still more SAV64s available. If you’re a member on Lemon, you can PM skidivingirl and she’ll get you all fixed up. There's more info over on Lemon about the SAV64.
Note: If the attached links lead to posts with “Sold” in the topic title, that means the pricing on that page is out of date. Regardless, skidivingirl is a very responsive and friendly cat, so don’t hesitate PM’ing her for info on the various forms she is active.