UPDATE: Searching online for rechargeable AAA batteries is interesting. A lot of companies (mostly Chinese) are advertising on eBay and Amazon, but you have to be careful. You search on "Lithium-Ion" and the results are Nickle Metal Hydride batteries. In fact, the odd form-factor of my bicycle headlight batteries is no accident - they produce a different voltage (3.7 volts) than most Alkaline batteries (1.5 volts). So the choice for recharagable batteries (that fit a standard AA or AAA slot today) is limited to NiMh, although one company makes a Lithium Ion AA battery with a voltage reducer built in.
It is a bit confusing for the average person!
UPDATE: I researched this further and some readers have been helpful. The problem for the NiMh batteries is that they are 1.2 volts, not 1.5 volts as with alkaline batteries. So you have to live with a slightly lower voltage, which should not affect most electronics.
Lithium-Ion, on the other hand, as I noted, are at 3.7 Volts, which means they are ill-suited for plug-and-play replacement with Alkaline batteries, unless some voltage correction is implemented.
Like I said, I think the ultimate answer is down the road - when new appliances come with built-in batteries, like your cell phone already does, instead of removable "cells".
As for Golf Carts, EZ-GO is indeed selling a Lithium-Ion cart, which will no doubt be the wave of the future. As for retrofitting older carts? Probably like trying to retrofit older appliances with newer batteries - just not cost-effective or convenient.