E.g. if 1/6 of miners are willing to accept your fee the time to get 6 confirmations is doubled on average. That way most users will only pay a fee that enough (but not most) miners will accept.
Incorrect. With 1/6 of miners accepting your fee, there is 1/6 chance your transaction will be included in the next block, thus on average your transactions will be 6 times slower.
It's 6 times slower for first confirmation, but from then on it's the regular rate, so it's only double the time for 6 confirmation.