Bitcoin fees were cut in half on a technical level by those that chose to adopt segwit which made transactions roughly half as big. Schnoor signatures can further compress transactions to get even more in a block.

If in spite of these innovations blocks end up full, a block size increase is still a tool kept in reserve.

In reality BCH did not make any hard won technical innovations and simply reached for the bigger blocks knob. If BCH did become the globally adopted winner its blocks would fill and create a fee market eventually too driving it to seek the same sorts of transaction size optimizations bitcoin has made. These roads might well converge in a similar place eventually.

I strongly suspect Layer 2 solutions are going to be needed regardless of the knobs fiddled on an expensive but immutable Layer 1 so we might as well all buckle up for that. Plus, atomic swaps in Lightning pave the way for decentralized exchanges which means even better anonymization and censorship resistance. Everyone wins with a stable Layer 2 most major coins are compatible with.