There is a theory that transaction fees paid externally represent an individual incentive that works counter to system security (incentive incompatible). The theory holds that a merchant paying a miner "off-chain" to confirm the merchant's transactions prevents other merchants' transactions from being confirmed, or that it raises the cost of those confirmations, giving advantage to those who accept such fees.

One impact of such arrangements is that an average historical fee rate cannot be determined through chain analysis. The apparent rate would be lower than the market rate. This could of course lead spenders to underestimate a sufficient fee. However there is no aspect of Bitcoin that requires future fees to equal some average of past fees. Estimation necessarily compensates, such as by ignoring "free" transactions in full blocks or using standard deviation to identify outliers. But fee estimation is just that, estimation. Actual fee levels are controlled by competition.

Another impact is that disparate relative fee levels can highlight certain transactions as being associated with such arrangements. This can contribute to taint of the merchant's transaction and/or the miner's coinbase. But given the arrangement is a choice made by the creators of these transactions, there is no privacy loss.

There is no impact on market fee rates or the ability of others to obtain confirmations. If the arrangement deviates from market rates then either the miner or the merchant is accepting an unnecessary loss. This is no different than the miner confirming transactions with below-market on-chain fees or the merchant overestimating on-chain fees, respectively. In any case there would be no harm to system security even if all fees were paid off chain.

Bitcoin provides a mechanism for on-chain fees so that a transaction can compensate any miner without the use of identity. It is a privacy-preserving convenience. If miners and merchants prefer to weaken their own privacy by performing additional tasks, there is no basis to consider that undesirable. This theory is therefore invalid.

Furthermore, the merchant must accept a delayed confirmation time inversely proportional to the miner’s hash power. The side-fee is offered at the market rate since the miner will incur an opportunity cost otherwise.

There is a related theory that side fee arrangements constitute a pooling pressure. If fees paid are consistent with the market there can be no effect on pooling. Above market fees are a state subsidy, as we must treat the subsidy as not economically rational. Below market fees are a tax, as we must treat the loss as involuntary. These are distortions just like any other state subsidy/tax and are therefore not unique to side fees. As such the existence of side fees does not create a new pooling pressure beyond what exists with on-chain fees, and the theory is therefore invalid.