There was only a single drop from 50 BTC to 25 BTC so there is no basis for your claim. And it can not work the way you describe. With 100k transactions per day and $0.10 fees per transactions miners can collect 3.65 million Dollars per year. So everyone with a handful million dollars to spare can easily completely destroy the Bitcoin network. Even better, there are already people with a lot of mining hardware out there, they would only have to pay electricity for a few weeks.
Have a look at the charts showing the fees per day [1] and the network deficit [2]. On the one hand fees went up, but before the block reward dropped, on the other hand the network operated at a deficit for quite some time. One has of course to take these graphs with a grain of salt because it is quite hard to estimated the real costs of running the Bitcoin network.
But I really don't understand what you are arguing for. Once the block reward becomes mostly irrelevant you have essentially two choices - relatively expensive transactions or a weak network, i.e. low hash rate. Don't you agree with that?
No, you're missing the point. If your narrative were true, we would see fee increases after every reward drop. Never happened.
This is how it actually works: reward drops -> unhappy miners quit -> difficulty drops -> cost per transaction drops.