It might happen more often than you think, with a 400mA fuse in a 60,000 count meter.
It depends..
Since I have DP831 and UT210E , i haven't measured current with meter that often.
When I do, I alternate between Brymens and MTX3293 (that has only one current input), and use Metrix for current measurements at desk mostly because of that. Which means I usually have no source to blow 10A fuse.
On equipment that runs lead acid accumulators, I mainly use UT210E, mostly because I don't need absolute precision and no need to disconnect wiring..
I blew exactly 3 fuses in meters in 40 years... First one, 40 years ago, scared the bejesus out of me.. Since then I'm really careful about any current measurements... Other 2 were measuring current on equipment connected to lead acid acccu, that while measuring drew too much current..
I also pretty much never rotate meter switch with voltage connected, even if I know it's perfectly safe.. I just have bad feeling in the stomach when I think about doing it... What can I say, childhood traumas....