This is a very common fault, yes. Power supply issues in general. It is also not uncommon for people to replace e.g. Wifi routers because the wall warts fail.

It comes down to a few people don't knowing a lot about it - and I'm not blaming anyone for that, we all have our interests and most people have more than enough to do already to worry about what goes on inside their stuff.

Also, electronics are, to a lot of people in a lot of places, so cheap that they would rather just curse a little and buy a new thing, instead of bothering with taking the thing to a shop. And of course a few hours of skilled labour in a big city in the west might also be almost as expensive as making a whole new TV in a factory in Asia plus shipping, so it might not even make economic sense.

Electrolytic capacitors are not solid state and likely #1 failure mode for most electronics. There are options for better (e.g. Al polymer) capacitors that are rather expensive - overall good capacitors are 'expensive', e.g. more than a dollar a piece in some cases.

The 2nd most common failure mode gotta be the mlcc (multi layer ceramic capacitor) cracks/shorts.

If your model was popular, there's likely a recap kit for its power supply. It usually makes senss to swap all the capacitors in the kit, unless the kit instructions say otherwise.

You can look for physical signs of degredation (bulgy, leaky, discolored), but to really test a capacitor for capacititance, you need to take it out of the circuit, at which point, you may as well put a new, high quality capacitor in.

The OEM capacitors may likely have a just right voltage rating, a new one with a higher voltage rating (and same capacitance, compatible type) may last longer in cirucit as well.

That would require some experience, yet the most common visual clue would be 'bulging'. There are some ways to measure ESR w/o desoldering but they won't be reliable at all times.

Measuring voltages, peak to peak, is a bit more work.