I have a flashlight that came with rechargeable 123s. The first set lasted two cycles, the replacements one. I bought a different brand of battery and charger locally, which seems to do ok. But I think I would limit the rechargeables to practice and utility, and keep a fresh set of Lithium batteries for carry. The rechargeables have a lower capacity and some self-discharge, so there is not as much light per cycle as with throwaways.
I have a couple of cheap fake tactical lights that take regular alkalines. The one I leave in my shooting bag for the occasional low light IDPA match came up flat the other day, with very little use. Either it self discharged or something in the bag leaned on the switch and ran it down.