Its a rare occurrence for purely wanting a marginally higher reward. That's not to say it won't happen because the 3rd place team is full of aimless sheep following an equally clueless person who happens to be running towards the 2nd place team, or the current 2nd place team spent most of the game getting greedy and back-capping 3rd place's points so they refuse to want to cooperate in a push against 1st place.
The same logic can be applied to two teams more frequently focusing-down 1st place if the rewards are even higher. So that is to say, nothing changes.
The path of least resistance to what though? If they want more mogtomes they'll pick a different, more lucrative content if they're trying to farm it. That's the path to least resistance. Not fight for 2nd place for the same amount of mogtomes you can get for getting rolled in Rival Wings.
To the Shatter example, red and blue converging on each other isn't because they're actively trying to sabotage each other instead of yellow (who I assume is in 1st in this situation?), it's because they're not totally braindead enough to follow them into their chokepoint while another team is right there, and lack the aptitude of knowing when to back-off; something most people queuing for FL seem to lack. Reducing 3rd place rewards keeps lethargic play from being productive as far as mogtomes are concerned. Seriously doubt people would put in that much effort to sabotage 2nd place for 2 more mogtomes and run the risk of they themselves landing in 3rd.