Deep mempool- lot of transactions waiting so the market will be quite congested, that’s when one most time need to pay high fee for their transactions to be selected by the miners.
Shallow mempool- one with less waiting transactions, in this case even small fee can get confirmed fast . Because at the market is less congested.
I perfectly understand what your message is here but it is clear to understand that even in a less congested mempool as you have clearly described I think you still need to pay high priority fee if you’re looking to get your transaction in the next block but this time around this high priority fee wouldn’t be much like during the high congested network.
For example the network is actually less congested now and fees less than 1 sats/vbyte are enough to get my transaction to be picked but if I am looking to get the transaction into the next available block then I have to pay high priority fee like the 1 sats/vbyte or a little bit higher so the miners treat it as high priority transaction. This is how it works even in more congested pool.
Also fast confirmation depends on two things, your transaction been picked in the next block and the block gets confirmed fast by the miner solving the puzzle fast. You can have your transaction picked the next block but the block might get delayed to be confirmed fast
Priority in fees is for occasions and needs.
Sometimes I use the lowest of fees, and my transactions get confirmed asap, even below the expected time. One thing is for sure when it comes to Bitcoin transactions: the network gives you a lot of options when it comes to transaction confirmation and fees.
The image below explains such features that give bitcoin users options and priorities in fees based on network congestion at the time of sending the transaction into the mempool.
