I think so, since there was a huge increase in the number of SegWit transactions in the last few months.
And note that such results are without Lightning Network.
I guess that, once ready, LN will give a hard time for altcoins out there that have low fees as their main selling point.
Coinbase started to use SegWit, which has a great impact on the network. Also, as I saw somewhere, they started to combine transactions into batches, this also lowers the transaction fees. (less transaction, less fee, because mempool is not full, so there's no need to increase the fees for a transaction in order to get it confirmed in time...
The Lightning Network will have a huge impact in speed and not in connection with the fees, because fees are low at the moment, later on if another bull market will come, then will the LN have impact on fees.