Except, these electrolytics are just handling AC line or audio
frequencies. They may have expired, but not from strain of 100KHz or
whatever.
Also, they aren't used in some highly-feedbacked circuit, as is the case
with switching supplies. Transistor radios use more electrolytics than
tube radios (which could be often diagnosed by listening to the radio, hum
meant a new filter capacitor, low audio gain meant a new cathode bypass
capacitor in the audio stages), but they are straightforward. They are
either bypassing the emitter resistor in the audio stages, coupling audio
between stages, or to provide a low impedance on the "B+" line. It's
daunting to look at, all those electrolytics in a transistor radio, but
you don't need anything fancy to replace them with, and if you aren't
going to troubleshoot (low audio, bad bypass or electrolytic coupling
capacitor, motorboating, bad electrolytic on the "B+" line), then just
replacing them all is relatively cheap (compared to buying an ESR meter)
and fairly fast.
Michael