Without mining rewards, would miners keep the network alive with just transaction fees, or would Bitcoin collapse?
This ain't happening bro!
The block reward will continue to be divided in half, and miners' rewards will continue to decrease as a result, while the earlier miners will enjoy more. The time of the fee hike will ensure more reward for miners as well. However, the further development (scaling) and adoption of the L2 will be a problem for miners. Though they will still gain, the reward will not be as though it was pushed through the L1 directly.
Eventually, fees should become bigger than the actual rewards, imo, but these days wouldn't be in our lifetimes, probably.
So miners would still be inclined to continue their honest work.