[alcio]

"miners somehowd eviate from the conventional wisdom or the norm, which dictates that transactions are prioritized for inclusion based on the fee-per-byte metric"

Miners prioritize by fee-per-byte, except that the on-chain fee only accounts for part of the fee paid for some transactions.

Over the years, many services have popped up where you can pay an out-of-band fee to a miner to include your transactions first.

Of course, this is detrimental to users not using these systems as it biases the algorithms used to determine what is the current best fee-per-byte to pay.

[oleganza]

Hopefully proper implementation of CPFP (child-pays-for-parent) on the miners' side and in the wallets would bring fully decentralized solution to the problem. So you could simply "bump" your transaction by sending a child one that pays higher feerate for both itself and the parent. That would be more efficient since that fee would go to all miners, not just those with the deals with "accelerators". And no one in between to collect extra fee.

[viraptor]

Why would people use one of them rather than increase the fee? Is it just for "forgot to do it, I'll pay extra now" situations, or is there a reason to do it anyway?

[alcio]

In some cases, increasing the fee once the transaction has been broadcast is not possible (original transaction doesn't use replace-by-fee OR child-pay-for-parent is not possible)

[pests]

As someone replied I researched a similar service years ago to get a friend's transaction unstuck. Usually just a credit card payment and the tx id and they mine it.