Exactly, it is better to consolidate coins inside wallets, but transactions to exchanges can be confirmed with fee set at 1 sat / byte. Weeks ago, my transaction confirmed after three or four days. It's cool.
Besides LoyceV's thread, I suggest to read mine:
Bitcoin Transaction Fees - Everything in onePlease remember to check mempool situation, and suggested fees on
https://coinb.in/#fees. Today, suggested fee rises to 19 satoshis/ byte, that is not a good day to consolidate your coins.
Additionally, time zone to move your coins should be considered too.
Time zones affect feesDetails below. In general, if you are not hurry, please choose the timezones at which fees usually are low to move your funds.
You can compare the data from this study with the data generated at Johoe's Mempool Statistics page:
https://jochen-hoenicke.de/queue/#1,2w. Here's a random 2 week sample I took from last September (click for full size):
The dates along the bottom are at midnight (00:00) UTC. So you can see from this sample, there is a spike in fees on most days between around 10:00 and 18:00 (when Europe and then later America are awake), at which point they start reducing, and hit a low point around 01:00 - 04:00 UTC. This certainly ties in with the data from OP's study.
It's something I've casually noticed, but never given much though to. But considering it now, I wouldn't have expected such a constant and similar drop given that China has more people than Europe and North America combined.