Everything you said is such a stretch of "nope" that it seems you're just trying to argue at this point.
Two players defeating an NPC at exactly the same time? That's a non issue. In the 1 in unnecessarily large number chance that happens, the comp can decide. That, or on the KotH channel you can have only one challenger battling at a time.
If it is a designated channel, players using non-comp teams are just fodder. It makes no sense to be on the channel battling the E-4 if you're not trying to win.
The time limit can be whatever or nothing at all. Whatever the devs decide.
As for the prize for holding the position, really? 60,000 P per hour is broken? 4 items from a prize pool per hour are broken? For one person per region? Okay. Let's say there are 96 items per day per region with my one every fifteen minutes model.
Of the 96, one is a master ball. 24 are single Rare Candies. Things like that. Again, nothing breaking the game. It's rewarding players for being the King of the Hill. I imagine the prize support and the appeal of being the champion... even the record board would draw players in. The 1,000 P per minute is so nominal at that level of play that it could be removed with no loss of interest.
The prize support should match the battle timer whatever it is. So thirty minutes becomes 48 per day. The problem there is that less people will challenge the incumbent champion if they have to wait around for half an hour. Though with E-4 cool-down times, it is probably a non issue.