The joystick config is available though REG 5: https://gitlab.com/SpectrumNext/ZX_Spectrum_Next_FPGA/-/blob/master/cores/zxnext/nextreg.txt#L99
the main problem with changing it is that users expect to be in control of it themselves. It’s not reset by the OS when you do a soft reset, only a hard reset.
A typical way round that is for a game to read the config, change it, read the sticks then immediately restore the config. Warhawk does that, for example.