The only rechargeable lithium technology is lithium-ion, which inherently runs at 3.7 or so volts output. There is no rechargeable lithium battery technology that runs at the 1.5-1.9 volts output of the typical lithium AA/AAA primary batteries. So the answer as to why they haven't done it is they don't know how yet.
Actually, one company *did* try to market rechargeable cells with a completely different chemistry. They were called PowerGenics, if I recall correctly; the batteries were a nickel-zinc chemistry, which has actually been around forever, PG just claimed to have overcome some of the limitations. Unlike pre-Eneloop NiMH cells, self discharge was low, and they were much more resistant to charge "memory" than NiCd, too.
Voltage was ~1.6V nominal, but something like 1.9V hot off the charger; this was a BIG problem when used in series in devices that expected 1.5V (alkaline) or 1.7V (Energizer Lithium) at most; I heard plenty of accounts from photographers that they fried their flash units using PG's NiZn batteries.
Unfortunately, NiZN cells required separate chargers. Also, they never fully overcame the chemistry's inherent flaws, such as limited recharge cycles, and deteriorating capacity with more cycles; just around the same time, Eneloops hit the market, so self-discharge was no longer a reason to not use NiMH any more, and PowerGenics closed up shop soon after.
----------------------------
UPDATE: After posting that, I thought I'd try googling PowerGenics and NiZn batteries. Turns out the company is still around, but I got the name wrong, it's PowerGenix; they *did* exit the consumer market, but are still marketing their NiZn cells for industrial use.
More on NiZn cells:
https://en.wikipedia.org/wiki/Nickel–zinc_battery
Kinda sad they never caught on, there's a lot to like for us flashoholics: high energy density, VERY high discharge rates, and high recharge rates (1C). Ah well…