transactions cheaper than that would also be getting included in blocks.
Absolutely. Have a look at this page:
https://mempool.space/. Blocks for the last 4 or 5 hours have been full, but if you scroll down to around block 634,000, there are plenty of blocks which aren't even close to being full, with some blocks as low as 30-50 kB. Since there is no reason for a miner not to fill up a block to maximize their profit from fees, transactions with fees lower than 1 sat/byte would absolutely be included in these blocks if they were being relayed.
Essentially, any time the mempool completely empties, there would have been room to include more transactions in the most recent block.