That’s true. For most electronic devices, PSU caps are most of the time the reason for a failure. Sometimes (more rarely) a power transistor is shorted or a regulator is dead. In this case the repair can be a bit more complicated because a shorted power component can destroy surrounding components like resistors or other active components.
I did revival a MOTU 828 interface just replacing chemical caps in it. I’ve seen devices, like Adams Smith Zeta Three synchronizers, with about ten dead capacitors in their power supply !
Chemical caps are dying because they become dry. Most of the time this can be seen watching for their case top. If it’s slightly domed, then it’s a sign of failure with almost 100% probability.
The quality of caps is important. Use Panasonic or other leader caps manufacturer for replacement, with the same or higher temperature specification (85 or 105°) or you could get the same problem very fast.
Another point is the PCB design. Sometimes it is necessary to modify the device ventilation to avoid capacitor heating. There are often design differences between high end manufacturers and low cost ones at this level. The first ones do take seriously into account components eating so that their devices lifespan is almost not affected by capacitors aging.
Capacitor aging is mostly a result of too much eating.
An old device not working anymore after a power off / power on is a clear sign of capacitor failure.