My power supply can be anything from a phone charger to 3 AA batteries or a power bank or , more often than not, my computer's USB port
That was first thing that came to me when I saw the USB download circuit in the manual was "why use a 3.5mm stereo plug and jack when the USB cable has access to 5v right there".
The PICAXE system was designed in the days before USB when everything was RS232 serial and PC's did not supply power for circuits and add-ons. The main way of getting power out of a PC back then was to use a plug-in pass-through adapter for the keyboard DIN connector which could extract 5V from that. But its capabilities were rarely well defined.
Initially the PICAXE used a 3-way Molex connector for programming and we sold a 9-way serial to Molex plug cable (AXE025+CON038). That evolved into using a stereo jack and 9-way to jack cable (AXE026) when digital cameras emerged and cheap cables for those arrived. That also explains why the jack is wired as it is, not how audio jacks would be - we needed the jack to match the cable wiring for such cameras.
The PICAXE system has stayed with using a three-pole jack to maintain compatibility with boards and projects from that era when USB came along. First as an extension for USB-to-9-way serial converters (USB010+AXE026) then as the dedicated all-in-one AXE027 cable.
Using USB to power projects is something which is possible but does have issues. Some USB sockets on some PC's supplied straight from the PSU, some fused, some not. This meant a wiring fault on a circuit board could potentially destroy a very expensive PC, even be a fire hazard. Some schools and other educational establishments won't allow connection to USB for that reason, sometimes won't even allow the use of mains power supplies, require the use of battery packs, only allow standard chemical batteries, not rechargeables.
USB battery packs are an option these days but many will turn off after a short while if the PICAXE circuit isn't drawing enough current, and can also be less than ideal if allowing high current when there is a wiring fault on the board.
We could make a USB PICAXE board, put the AXE027 interface on the board along with a PSU which ensures powering via USB as safe as it can be but that would push up the price of such boards, and they wouldn't be bought or used by those who don't allow USB connections, and many will see it as an additional cost not worth paying.
There has never really been a business case for doing that so we have stuck with the, now well established, tried and tested, jack socket for download, leaving the end-user to decide how they will power the boards.