I take exception to the common wisdom that FDM printers have XY tolerances in the range 0.1 to 0.5 mm. That might have been the case 5 or 6 years ago, but with a modern printer, you expect tool positioning accuracy and reproducibility (layers lining up) on the order of 10 microns (0.01 mm). The major source of inexactness is extrusion width, due to the cross sections of your extrusions not being perfect rectangles, but bulging at the sides in a shape like two matching parentheses and their convex hull ( ).
One reason I bring this up is that one of the most important uses of calipers with FDM printing is to calibrate your extrusion multiplier to compensate for these effects. If you can only measure in 0.1 mm increments, measuring printed perimeters is just going to come out the nominal 0.4 mm or whatever, unless things are more than 15% or so off. That's a big relative error that will have consequences in terms of solid layers coming out with gaps or coming out over-filled and colliding with the nozzle as it digs them upward. With 0.01 mm measurement increments, you can get your extrusion right within 1%. This makes a big difference to your ability to print parts that fit the first time rather than needing trial-and-error refinement.
As for actually making things, if they're going to fit together with other real-world stuff, they need to be made with significant adjustability or with precise measurements. Often adjustability is the way to go when you can, but for printing replacement parts this often isn't an option. And if you need parts to match for a snap fit, interference fit, holding gears or bearings in a particular place without backlash, etc., measuring to the nearest 0.1 mm is not going to cut it. Especially with digital calipers, seeing a measurement like 10.2 doesn't tell you whether it's actually 10.151 or 10.249, or even further off if the calipers are low quality (which the ones that only show 0.1 mm scale tend to be). I found that upgrading to higher quality 0.01 mm scale digital calipers made a huge difference to my ability to just "get stuff done" with 3D printing, without having to re-print over and over tweaking dimensions. Particular applications that come to mind where it made a difference for me were:
Enclosures for PCBs/SBCs.
Upgrades/add-ons for printers: brackets to mount things to the aluminum extrusions, fan ducts, etc.
Small plastic pieces to reinforce laptops & other electronics where screw points on housing were broken.
Lids to pop in and seal against gaskets in air-tight bins.
Feet to fit snug on metal furniture legs.
Finally, even if in practice FDM printers can only meet mediocre tolerances, being off by something like 0.05 mm or even 0.1 mm from a known good measurement is a lot better than being off by that much from a measurement that itself was already off by nearly 0.1 mm.
