APU AOs regularly travel in cabs, as again they think they’re slightly better than everyone else because they’re plain clothed! so people that don’t have the proper authority travel in cabs all the time.
Are you talking about during work hours or after work? During working hours, APU usually travel in cars. When they do take the train, they're out looking for graffers and new graffiti on the line, you get the best vantage point from the cab. From the windows in the carriage, you aren't likely to see as much especially at night when you see bugger all.
They don't think they're better than everyone because they're plain clothed, they think they're better than everyone because their job largely consists of driving around, sitting about, booking someone once a fortnight, and getting heaps of praise for it

My contention is that it already happens, so ‘brendan03’, take your pre-set ways of thinking somewhere else. Sure sometimes rules are bent, but this is an everyday occurrence. If the two are happy enough to travel together, then I’m sure you can charge your HHDs as well.
AO's are allowed to travel in cabs (according to the Transport Regs.) but it is ultimately up to the driver. Cabs aren't particularly spacious to begin with, the HHD's and their chargers aren't small, and there would be cables everywhere. It just isn't practical. Sometimes it's on as soon as you walk into the train, no time to shuffle into a cab to get a HHD. The same goes for getting off the train, it isn't always a leisurely exit. No time for logging on/off. You'd also have passengers following you in, not always with the best intentions either.
Human nature (and AO's are human, or so they tell me) dictates laziness and complacency, so you'd have AO's not replacing HHD's because they can't be stuffed. Some trains would have none, some would have too many, most not charging.