think about it if you were a miner, and have learnt that you can charge XXX for transaction why would you be happy to again charge just one X?
It is certain the more popular coins will increase costs to catch up with bitcoin, as opposed to bitcoin lowering .
Developers are already being pressured to behave in ways that I dare not repeat.
as more miners enter the space you will have to reduce your price if you want to get paid. this is how supply and demand works. so no, transaction fees won't stay the same price forever.