Miners fees make up .3% of the money miners make, meaning that if the fees raised by 100x then miners would still only make a third of what they make now. Which in fantasy land means that miners just gracefully exit and cease to exist, but really means you now have a drop of hash rate and also a group of people with machines that make hashrate that got fucked over by bitcoin and have no wish for it to succeed.
You fail to understand the fact that the overall transaction volume is low now. When TX volume increases the overall amount of TX fees will also increase. Also when transaction volume increases the price of bitcoin is likely to increase as more commerce will generally mean higher demand for bitcoin.
The point remains, though. To retain the status quo, the product of transaction volume, fee per transaction, and value of BTC, needs to increase 300-fold. That's a big increase to be depending on.
Another point is that miners will likely see increases in efficiency over time, so when the block subsidy is reduced it will have little effect on the ongoing profitability of the miners as they will be able to use this added efficiency to have lower electric costs.
That would decrease security, though. Efficiency benefits miners and attackers equally, so if miners take advantage of it to reduce their costs, attackers can mount a given attack more cheaply.
Sorry, all you altcoin supporters, but it's true. None of the others matter one lick, and in the not-too-distant future, none of the current altcoins will even exist, as far as the world is concerned.
Certainly all the Proof-of-Work altcoins have the same problem. The "work" part costs money, and that ultimately must come from either high inflation or high fees. (That is, either savers or spenders.)
In the long run, Proof-of-Work can't compete with Proof-of-Stake.