I only worked in the air so I can't say how the computer reservations system works, especially with other companies. We did have it happen and we did have to reseat and yes, it sometimes got missed at check-in (grrrrr!)

For us it was easy because I think it only affected one aircraft type (two?) and only those seated on the side. There were two seats together and each had only one extra O2 so we knew if two parents with lap babies sat in them... It also wasn't an issue if the flight wasn't full.

How many lap babies are allowed in each row should be registered and people who try to book those seats would say, get a pop up saying that the lap baby max has been reached for this row, or similar. The problem is simply that this doesn't happen very often. Remember that a solo parent with two under-2's can only have one on the lap. The other has to have a seat so they wouldn't be affected.

Perhaps twin parents should rally on this issue and get the airlines to include this in their reservation system. I can't imagine this is that difficult a program to write.