Assume BCH does not exist, BTC will still face a high fee.

What do numbers from the previous year show?

First plot shows the confirmed transactions per day in MB, which is more relevant than number of translations per day because any blockchain cares about a size of blocks in MB. If hashrate matches a nominal hashrate(144 MB per day = 1MB blocksize * 6 per hour * 24 hours) defined by difficulty, blue and red line are overlapped. First plot shows, since December 1st 2017, hashrate is higher than the nominal hashrate(blue above red), which means new machines mined more than 144MB per day and clean overloaded mempool.

Second plot shows the BTC mempool in MB. Blue line below red line in the first plot would show an increase in the mempool size(high fee). For example, you can see it in end of August 2017 and November 2017.

Lightning network of BTC increases a blocksize ~ 1,05MB (5%) https://blockchain.info/charts/avg-block-size and perhaps reduces number of transactions on the BTC blockchain ~5% https://blockchain.info/charts/n-transactions. The BTC usage drops due to high fee as well.

New hashrate is driven by BTC price. Current BTC price slows down demand for new miners and soon we will not see a new hashpower, so blue line will not be above red line and mempool will be full again, thus BTC fee will be high again! This scenario excludes an existence of BCH, which makes the BTC future even worse.

If price goes UP, hashrate goes UP. Everything looks fine but this is a positive feedback loop and it has to hit a wall!