AFAIK the only way to do want would be to buy an unflashed bootleg cartridge, like they ones they used to use to inject Pokemon ROMS in the GBA days. Even then though, it's a one and done kind of thing since it's already been said they are Read-Only, as are most commercial media. Also the reason why mod redirection is a thing. I'm curious as to WHY you'd want to do this anyway? Since these "medias" can be decrypted, dumped, edited, rebuilt, installed and played why would someone want to flash them to cartridges just to have a bunch lying around? So yeah I would say your best and probably only option is to find some blank cartridge mediums and flash your ROMs to it, again it can only be done once so I don't see how useful that is unless you can find some RW ones but I'm not sure they exist.
Even if you did though, unless the console can recognize the medium it's not really going to matter. I can burn ISO's of PS3 games all day but they won't play without CFW and only then it's because they can natively read R/W discs.