I'm okay with cutting the golf and tennis just because here in the US we already get enough of it on any given weekend. But each nation does vary...Nope, just a different way of accumulating medals. And diving used to be one of the big televised events in the days of Greg Louganis. It has been very scarce on TV now that the victories have dried up. I expect a similar fate in the future if Beach Volleyball no longer brings the medal haul. TV coverage on NBC is typically proportional to the quality of the Americans competing in the sport.
Good rule. It would get rid of the worst offenders right off the bat. Bye-Bye Tennis, Golf, Boxing, and Baseball.
I am not necessarily for chopping smaller sports like Weighlifting or shooting. But I would be willing to cut some of the medals given. They could probably survive with fewer weight classes and shooting disciplines.
I like the Olympics because I get to see some sports that are not normally televised here. It's a whole different adventure.
EDIT - right now I'm watching some of that climbing stuff, it's fascinating. It's almost like running, except they have to make time/speed in a vertical fashion using their arms as well as their legs. It's fascinating indeed.