PICAXE with USB on-chip may one day be possible but there are wider technical issues as well as just providing firmware and drivers. The higher USB protocols have 'keep alive' handshaking and have to be responded to or adverse effects can occur within the host OS; the USB device gets flagged as not working or become dismounted and no longer accessible.
As a PICmicro / PICAXE can only do one thing at a time, if it's in a blocking or timing command it cannot respond to those handshakes and if it does respond the PICAXE can consequently miss data and have incorrect timing. Resolving that conflict of requirements is not simple and may prove impossible.
The current trend seems to be for companies to provide development boards with FTDI USB-to-serial chips on-board so they appear to only require a USB-to-USB cable. That reduces the cable requirements its cost but ups the complexity of boards and their cost. To save having an FTDI chip per-PICAXE, to allow the current ease of use of PICAXE on bread-board and strip-board, a single FTDI chip can be moved between PICAXE's as needed, and, to make that even simpler, the FTDI chip can be included within the USB cable, and we're back to the AXE027.