I didn't put words into erik's mouth. I linked to what erik posted and you can read them yourself. He even posted essentially the same thoughts in this topic (but didn't go into the whole backstory which you can read in that topic). I have also read his posts in other topics about the same thing, so while I can't say he won't ever make changes, for certain, the basis for that idea is certainly supported by previous statements.
But as I said you are free to come up with ideas on how to implement something that would work. There are a lot of basic combinations where the FIDE implementation is super easy to check, though, it would take a little thought experiment (or setting up positions) to make sure there aren't positions where those rules fail.
The check only comes about with K+B, K+N and K+2N. If the side with no time has one pawn, or at least one pawn, then mate would be possible in the vast majority of cases. Even with additional material, and at least one pawn, the mate would still be possible, but there might be some instances where it isn't.
Same material and the side has only a queen, mate is possible only with 2N (edited 8/25)
Same material and only a knight, mate is possible.
Same material and only a rook, mate would be possible with the knight and two knights but not the bishop.
Same material and only a bishop, mate would be possible with a knight (or 2 knights) or a bishop of opposite color.
However, there are likely some configurations of even those combinations, where mate would not be possible and the simple material check like the site has now would not be sufficient to find.
Without making such code it is all just assumption. now let us please try to fix the code and make this program more towards chess rather than what one sole country's chess federation thinks chess should be. btw the link you show litterally has Erik saying the program should be more emcompassing and not that everything should remain as is. Perhaps it is better to not put words in Erik's mouth and let him speak for himself rather than having him portrayed to match your own opinions.