I could easily imagine the US military deploying autonomous combat bots to some middle-eastern country unaccompanied by human troops. They would care approximately zero about wasted ammo, and we already know from our drone strike policy what the military thinks about accidentally killing non-combatants. As long as there are no Americans around to get killed by rogue bots, it doesn't really matter how much collateral damage they cause, within reason.
I'm pretty skeptical the U.S. military is concerned about wasted ammunition. They waste so much on training and preparation that anything wasted in combat is minimal.
> I'm pretty sure the first side to allow fully autonomous weapons will do so before the technology is ready
It doesn't have to be autonomous to be deployed before it's ready. Iran managed to should down a civil aircraft based on human error. The U.S. has done the same decades earlier. Clearly there were either technology or human process problems, I suspect that autonomous military robots will follow this trend.
They may not care about the ammunition itself so much but they care about budget and combat effectiveness. It's not uncommon to have training be missed due to ammunition budget shortfalls and a robot without ammunition isn't terribly effective.
It's not something that's unique to autonomous systems, though I suppose it might terrify some people a bit more than when it's humans doing it.
You're making the bold assumption that the robots will actually work, instead of wasting ammunition on all the wrong targets, including friendlies. I'm pretty sure the first side to allow fully autonomous weapons will do so before the technology is ready (humans are never patient enough to wait until the technology is ready) and end up regretting it.