The actual problem comes next if transactions continue to ramp up as they have progressively leading to a backlog which never clears.
Personally, I'm not anxious for all that spam to be "cleared" by getting included in the blockchain.
It would be like having the street outside your house filled with trash and considering collecting them inside your house to "clean the street".
When the network is spammed, two things can happen, or both of them to some degree.
1) the blockchain will get bloated with spam
2) the mempool will get bloated with spam
Then it doesn't matter what price your wallet chooses, it will not guarantee inclusion by a miner, as the next person putting a transaction in will out bid you (yay fee market!).
This is only theoretical and provided all 1mb is legit use.
Practice shows that even at "extreme" load, fees don't rise above 5-6 cents.
The answer is simple: Legit txs are way below 1mb and the rest is topped off with spam. So there is no reason for fee competition at the top, as legit txs always outbid the spammers (provided their software is not crap).
What you say would happen, if indeed there was sufficient legit demand to cover the 1mb (which, unfortunately, there isn't). The time when this will be so is coming but by the time legit activity hits 1mb in a year or so, or later, we'll be at 1.7mb or more, so, again, it won't matter.
Being economically naive you would hurrah! at a working fee market. But actually by enforcing limited transactional scarcity with a blocksize cap what you actually do is break bitcoin for most people. Suddenly stuck transactions are widespread and sure you can still use bitcoin but fees will simply spiral upwards until they are ridiculous.
This is FUD (explained above why it has never worked that way).
The best bit is that as the network becomes increasingly congested actually performing a flooding attack to completely disrupt the network becomes trivially cheap to employ.
The network will still process the best paying 250.000 txs per day, undisrupted, no matter how much one floods/spams it.