Average Joe doesn't know how to set the default browser from the OS, so browsers provide this option so they can be sure that
they've done what's necessary for the user to choose them as the
This way they get a way bigger chance of getting users and the more users (AKA clients) they get the more money they make.
Application type and differentiation
tl;dr: "Inertia" effect doesn't applies to every type of application.
Comparing browsers with other types of applications, all known browsers offer more or less the same service so users can jump from one to another with
almost null adaptation so being the default one is a key point.
Taking your example: the people who frequently use a Image/Video Editor choose it for specific reasons which make them prefer one over the other, e.g. they have different capabilities, usability, integration with other apps, price, etc.
They will not start using one particular application just because they've been received the option of setting that program as default.
Other type of application that could relay on the "inertia" effect are (or used to be at least) the music players. The most people just want to use play-pause and hear the music, something that you can do it with every music player.
What would you do?
If you'd want to promote your own browser and get as much users as you can, would you let the task of asking about the default to the OS?
Would you try every OS to see if them work as you expect?
Even if it works in almost all the cases, would you "leave an open window" knowing that your competitors are including this option and you're probably not?