If you were traveling at 120 MPH and then accelerated to 156 MPH you would not say that this was a small difference without consequences.
It mattered significantly, in several respects. E.g. https://bitinfocharts.com/comparison/bitcoin-transactionfees...
Increasing supply above demand radically drops fee rates. That is the logical, predicted, and observed behavior-- both in Bitcoin and in other similar systems.
The current fees are well above the marginal transaction costs of processing and storing those transactions. (I estimated it was 3cents/kB, assuming GB scale blocks on ~1000 4U (36 bay) servers with 10Gbps networking distributed world-wide.) Other analysis I have seen erroneously assumes the POW is a marginal cost: which is only true with a tiny, limited, block-size.
During the September 1, 2018 "stress test" on the BCH network, the average transaction cost actually went down. All while the network processed 2 million transactions in a day.