I have an Iphone 7 running iOS 13.6.1, and I've also experienced these crashes, and would like to give some more info on what I've noticed about them.
I've seen them happen on practically any page / window. Not only when starting a prize fight, but also commonly when opening the CoC or Friends List, and occasionally when viewing a Fighter's full page. Haven't seen it happen on Daily Events yet though. But I think all these crashes are related due to the second thing I've noticed.
They seem to happen when navigating quickly through different screens and menus. I've noticed it often when returning to Prize Fights after checking the CoC and sending gifts to friends. But it never seems to happen if I stick to the same mode / menu for an extended period, like when I'm clearing one of the dailies and just going from one fight to the next. If it does crash when starting a prize fight it's always on the first fight after entering that mode from the Main Menu.
One example would be: Starting at the Prize Fight menu > Main Menu > Friends List > CoC > Open Relics > Main Menu > Prize Fight menu > Crash when starting a fight. All actions within 1-2 minutes of each other.
Another would be: Starting at Daily Events > Main Menu > Collection > Sell some moves > Main Menu > CoC > Crash when opening Friends List. All actions within 1-2 minutes of each other.
I'll try and pay closer attention to what I was looking at the moment before it happens to see if it's related to any single menu / page, but so far it just seems to be an issue with quickly switching between things. Maybe it's a bug relating to too many server calls too quickly, or with the Main Menu itself? Who knows, certainly not me.
EDIT: Also worth mentioning that I haven't experienced the PF crashes as often as other folks seem to (only around 3-5 times since they started happening), even though I have an older phone so I'm not sure it's a hardware issue. Lots of crashes on other menus, mostly Friends List and CoC, but very few on the actual PFs. Could be due to some differences in how I use the app and menus, but it's still worth mentioning.