1 sat/byte is definitely on the lowest spectrum of the average fee for the last few months. This is why I added the URL :
https://bitcoinfees.info/ for you to see what the average was over a longer period.
Not to go too far off-topic but that chart is "Historic daily average Bitcoin transaction fees". Obviously, the average is a lot higher than the 'minimum required' as a lot of services pump out high fee transactions and pass the cost on to their customers regardless of the state of the mempool.
Anyway, when I am consolidating inputs I wait until I can get 1 sat/byte before doing it.