then maybe that algorithm is correct because they are choosing all the highest fees to mine and then the lowest fees. Right now if you check mempool you will see a total of over 122.17 MvB for transactions under 10 sat/vByte which is need over 120 blocks to mine all of that and if you want to get your transaction got confirmation faster then use a high fee for your transaction or wait until your turn to get in a block.

There is no "correct" or "wrong" algorithm for this problem, rather an "optimal" algorithm. I think we can just assume that miners want to maximize their profit, but a greedy algorithm might not be optimal. E.g. see example posted before with the 10.1sat/byte example and https://en.wikipedia.org/wiki/Greedy_algorithm#Cases_of_failure

"wait until your turn" -> not sure what you mean here. That's exactly what I asked in my original post, i.e. if transaction age is a factor. If age is not a factor (which makes sense, since miners don't care and just prioritize higher fee transactions) then there's no notion of a "turn".

Miners are free to use any algorithm they like in order to choose which transactions to include in their candidate blocks.

In general however, then yes, miners simply prioritize the transactions in their mempool which have the highest fee rate. There are a few exceptions to this - for example mining pools will also include their own transactions with very low fees, Binance pool includes transactions made by the Binance exchange with low fees, they may include transactions they have been paid privately to include, and so on. However, these types of transactions usually only make a small handful of the total number in the block, with the vast majority of transactions simply being prioritized based on their fee rate.