We don't use them as our only mechanical cutting tool but they are used on nearly every cutting operation we do at some point.
For lifting chipboard or WBP Plywood flooring we use a circular saw as our main tool like most will do no doubt. The Fein is used to cut the corners neatly, avoiding having to overlap cuts like you need to with a circular saw.
Equally, when replacing a chipboard floor in a bathroom the Fein will be used to cut the flooring flush with the walls where it runs under them. Again, this is impossible with any circular saw or other type of saw on the market.
The Fein is the fastest way I have found to lift individual boards in a floor comprised of tongue and groove floorboards. No circular saw or any other tool necessary here.
Cutting copper pipes where you can't get a pipe cutter into, just whiz the Fein through them then deburr with a file. This has got me out of a difficult situation on many occasions.
Trimming architraves that are already fixed in order to fit a tiled floor under them, use the Fein again.
Removing skirting boards, now a quick job. Cut them down the middle then you can easily pull each piece out. Even better for removing them behind radiator pipework.
Cutting into a section of tiling on a stud wall to create an access panel because the previous plumber never bothered with them, just use the Fein again and cut straight through the grout line.
Not to mention how much tidier they are than a circular saw - because of how they cut and the thin blade very little dust is created.
I could list so many more time saving uses for this. It's the best tool we own.