Bitcoin cash did pretty well the last bull run. BCH had an higher number of transactions per day than BTC, LTC or XMR.
Source: https://bitinfocharts.com/comparison/transactions-btc-ltc-bch-xmr.html#6m
This should be a good empirical way to prove how big blocks are a good way to scale, but no. All volume in the BCH blockchain is fake volumen, all transactions are spam.
This is the classical maximalist defense against BCH processing more transactions than BTC. The criteria use to classify volume as spam is random, so we can say that all BTC and LN transactions are spam using exactly the same criteria. But this is not the actual issue:
There is no spam in a permissionless blockchain
Spamming can be defined as "unsolicited or undesired electronic messages". When we use the word undesired, we are making a moral/ethical judgement. In a permissionless blockchain, no one can classify transactions as undesired and even less decide what is allowed/denied.
We can just face 3 paradigms:
Transactions pay 1 sat/B or more: go into the next block.
The number of transactions are so high that the network can't handle it: Bitcoin cash has failed.
Someone is attacking the network sending huge amounts of <1 sat/B transactions and the network can't handle it (DoS attack): Bitcoin cash has failed.
As simple as that.