I don't think so why did you say that. How small fee makes transaction faster. You know if you put high priority fee the transaction made faster, even you put a large amount of btc but if you put a large amount then you choose a low-priority to only spend small fee the confirmation will take some time. So, for me, small fee doesn't matter.
Exactly, it is the same with everything.
The bigger bounty you give for completing some task, the bigger chance you have that someone will do it faster.
Same thing is about mining, miners have priorities of the transaction with the highest fee ( as a reward ), so they confirm the biggest fees transaction at the first place.
That is the reason why you may wait even for a week if you put up really small fee, because no one will want to confirm it because of the small bounty for miners.
I always prefer to put up higher fees just to have sure that my transaction will be confirmed pretty quick.