It's usually the current surge associated with initial capacitor charging as the amp starts up that blows the fuse. Repeated surges can fatigue the fuse, causing it to blow after nnn startups. I've seen power amplifier's own fuses blowing because a purchase agent found a deal on the same value fuse, but it was not rated for the repetitive surge. Replacing an MDL fuse with an AGC may not work out in the long term, but the unit might start up immediately after the replacement.

At my university we had an ancient computer with a HUGE capacitor bank in the power supply. "Brute force" was a very apt description for this 19V power supply. Unfortunately, after several dozen startup's the transformer primary  winding would open or the diode bank would fail. The secondary winding was a giggle because it looked like a 1/2" copper plate. It was a bad day for the service engineer called to replace that transformer because it was rumored to weigh about 800 pounds. We never shut the computer down, but power grid failures would apply towards our startup count.

Tube equipment typically presents less current draw at startup and is much more tolerant of voltage spikes. Up to the point of melting or breaking a weld, tubes will usually survive repeated gross abuse very well.

Surge protectors that offer an "Amplifier" outlet can provide a higher current path, less stringent filtering, or startup sequencing options for this outlet. Typically, power amplifiers are less sensitive to power line conducted noise. There may be several filters in series with a bank of receptacles associated with each stage. The "Amplifier" bank is first in the line, while CD players, phono preamps, and such will use the final stage for maximum suppression.