An interesting paper was recently shared on Research Pulse that showcases the predominance of out-of-band payments. Since transaction ordering within an Ethereum block can greatly impact the profitability of arbitrageurs, there has been anecdotal evidence of traders paying miners directly via out-of-band payments (outside of block rewards) to have their transactions included first.
The paper validates the notion that out-of-band payments do occur. It found that the 21 most prominent mining pools on Ethereum, which combined control over 50% of the hashrate, do include transactions in their blocks that were never sent to the mempool. A caveat is that the data also seems to include payouts from mining pools to individual miners.
Even in light of miner payouts, this implies that there is an already-existing direct relationship between 3rd parites and Ethereum miners. In the context of EIP1559, this relationship may strengthen since miner payouts would be affected by fee burning. As a response, miners could further collude with such 3rd parties to require out-of-band payments in addition to a base fee. Tips would only affect transaction inclusion if they are higher than such out-of-band payments.
This is perhaps a reason to evaluate the implementation of EIP1559 exclusively on ETH2, as opposed to ETH1.