Replacing both stats and elements isn't an hour of work anywhere that I know of. It can take hours sometimes just to get the water out of the tank.
Here, with our sediment problems, it can take several hours to clean the tanks. Sometimes, it's less than a gallon, sometimes, it's as much as seven - all through the element hole.
Today, I had to go out and diagnose a heater. It was in a commericial application (dog washing and grooming) and I had just worked on it about a year ago.
Diagnose water heater: $89.
That involves first checking for power, then removing the wires from the elements and checking for continuity through the elements, no continuity from element to tank. Replace everything and check amperage on the working elements.
I learned that when you have a lot of lime sediment in the tank, you must always check the interior of the tank behind the bottom thermostat - the lime can stick there and insulate the t-stat from the temp of the water and cause it to overheat.
Also, when it's a State with a poly liner, the liner could have been damaged by a dry fire install and it can form a pocket behind the element and stat. I saw one of those making a good head of steam once.
And you have to keep in mind that the thermostats are not always accurate as to temperature, and they might work one time and not the next. So, yes, it's probably a good idea to change them both if the button is popping.