Of course you can. There's a good amount of homebrew out there for various retro systems and a good chunk of those will sell you the ROM to download or even offer a physical cart. If you drive enough hype you can even make money porting it to newer platforms, e.g Pier Solar which was originally a homebrew Sega Genesis game but now has ports to several modernish platforms like PS3, PS4 and Steam.
We've also seen "new" retro systems like the Playdate.
Depending on the platform, easy enough to bypass lockout. The traditional way to lock out old consoles is to require you to include some material with a Nintendo copyright or trademark on the cartridge. That way, Nintendo can sue unlicensed game developers for copyright or trademark infringement. Various systems of this kind have been bypassed without the use of infringing material.
The lockout circuit on the NES, for example, can be bypassed by sending it a negative voltage spike. You can put the circutry on your cartridge.
We've also seen "new" retro systems like the Playdate.