If the fees increase less people will use bitcoin, which means that the bitcoin price will decrease.
When the block reward dissapears after all btc mined,the fees will have to increase in order to keep the mining profitable.
If the mining isn`t profitable,who will handle all the transactions?
This means that the bitcoin price will have to reach the sky,or bitcoin will die.
Many use Bitcoin as asset, as store of value or investment.
For them Bitcoin price rise to the sky is just fine.
However, if Bitcoin cease to be a coin, miners (and the network security) will be in trouble: whatever big will be the price of Bitcoin, if it doesn't circulate there will not be tx fee at all. No reward, no mining, and so on..
I hope that the system will auto-adjust itself and survive. Actually Satoshi thought of this problem and we have the halving, which is a good way to prepare, slowly, everybody to what's to come.