Does a usb rechargeable (as in the body itself plugs in, so battery charges in situ) with an acceptable light output exist?
I’ve got a couple of those eBay cheapies, and although they are ok the led isn’t overly bright and has a noticeable blue tint …. Output nowhere near as bright as my old ultra fire zoomable… So, is there something superior out there?
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What is acceptable? 200 lumens? 2000 lumens?
My Sofirn SC21 Pro is usb-c rechargable and is bright enough to be my EDC. Maybe my criteria are not the same as yours.
If more lumens or runtime are desired there are other lights from many brands that fulfill the needs of others.
Or maybe I don’t understand the question.
They exist for some flashlights, but I don’t know much about AA or 14500 flashlights.
I do know that many flashlights work best either on AA batteries, or on 14500 cells.
There’s not a whole lot of flashlights that work really well with both battery chemistries. 
I don’t think it lumens so much (200 or so would be ample)… I think it’s more that the led in the cheapie’s I have isn’t particularly good.
Basically I’d like something that emits a nice white light. Considering the cheapie rechargeable and my ultrafire both use a single 14500 the light output is miles apart - like chalk n cheese!
Being one of those (cheapies) is likely one of the problems.
What is the upper limit you want to spend?
About £20 … alas I’m only on a small pension nowadays
If I could find something that performs as well as the ultrafire (zs2…I think?) but actually had usb charging that would be perfect 
AA or 14500 and USB charging is a fairly rare combination. A few of these aren’t standard flashlights; a few are unreasonably large for the battery type; none have been especially popular with enthusiasts. One of the Lumintops is probably the best bet.
A few more options use USB-magnetic charging, which of course requires having the proprietary cable available when you need to charge. The Skilhunt M150 (preferably with Nichia 519A) is a nice option.
If that battery size isn’t a requirement, there are a lot of options with 18650 and 21700 batteries.