From these premise I draw the conclusion that the amount of hashing power in the system (premise #3) will directly correlate with the amount of transactional fee’s in the system (premise #1), and hence the security of the system (premise #2).
You're assuming that miners are completely distinct from the people who want the network to be secure (users/merchants/exchanges/etc).
That is a bad assumption. Nothing stops a merchant who wants more network security from either subsidizing miners (maybe in exchange for a promise to prioritize transactions to them) or mining themselves.
This is already happening, not for reasons of security but for other reasons.