It's possible, yes - obviously for the BBC Master only, not BBC B or Compact (which didn't have cartridge slots).
I've actually had a run of rom boards made up (that fit inside original Acorn cartridge cases or 3D printed cartridge cases) which I intend to use with my BBC Masters / Electrons at gaming events, so games can be changed by physically swapping cartridges around (whether I allow visitors to do this would be another matter; because hot swapping cartridges without power cycling the machine could potentially fry the cartridge!).
I do intend to get cartridges made up for some of the homebrew games/conversions, such as Tricky's stunning versions of Frogger/Carnival/Centipede etc, however with regards to producing a 'run' of them; I really don't know how much demand there would be (if any) as the cost of producing a game on ROM Cartridge would be comparatively expensive: there'd be a cost for the rom board, the rom, the cartridge case, packaging (if folks want a fancy 'box'), shipping etc. I haven't even looked at costings yet but the price of a single game on cartridge could easily retail at £20+ i.e. roughly the same price as buying an MMC-based product, which would contain the /entire/ BBC software library, not just one game!
It would be much easier (and cheaper) to package them on 5.25" floppy discs in nice, authentic wallets ...
Anyway, I don't wish to derail Snuggsy's Pooyan thread, but feel free to PM me or start another thread if you'd like more info about packaging games on physical media, as that's one area I have some expertise in ...
