Without side chains will transaction fees rise as block rewards fall? Transaction fees are currently minuscule when compared to block rewards. Even if transaction volume was 10x higher than it is now, this would be the case.

Is there any realistic scenario where transaction fees will not rise substantially to compensate miners for the effort as block rewards continue to fall over the next decade?
You are correct that transaction fees per block are much smaller than block reward, but they are still significant and rising:

https://www.smartbit.com.au/charts/transaction-fees-per-block

Recently the average has passed 0.5 BTC per block. With a 50x rise (easily obtainable if bitcoin use becomes mainstream in certain sectors) the reward would be 25BTC per block based on current fees staying the same.

This would be possible on chain with the combination of SegWit and a higher block size.

Side chains can help slow the growth of the blockchain but how much that is needed and its impact on Bitcoin miner fees remains unclear.