What rivalry?
And field hockey was the only team sport that was in consideration of being dropped back in 2013 (ultimately wrestling got the boot). That's why they went to 4 quarters, to make the game more interesting? If field hockey was ranked last, its unlikely to have changed. So for any team sport to have hope of being on the Olympic program, it has to hope another team sport is dropped, ie field hockey.
"Tuesday's decision came via secret ballot over four rounds, with 14 members voting each time on which sport should not be included in the core group. IOC President Jacques Rogge did not vote. Three sports were left in the final round: wrestling, field hockey and modern pentathlon."
Source
Personally, I would cut men's football to 12 teams, and ask all other team sports to cut rosters by 1 (except water polo, as it already has been cut) to get extra athlete quotas. However, I doubt that would ever happen.