Are Bitcoin transaction fees competitive?
There is no advantage or disadvantage for miners to include transactions, except for:

If they don't include transactions they don't receive the fees (which are still dwarfed by subsidy for now, but perhaps not forever), though fees can also be paid out of band.
It takes some time to build a block candidate with new transactions immediately after learning about another miner having broadcast another block. This time is short, but nonetheless nontrivial and may represent a loss of income (through subsidy) if it is wasted. Some miners therefore start working on an empty block immediately (which is certainly valid), and only in a second step switch to a candidate that includes transactions.

Bitcoin's consensus rules have no hardcoded amounts in them besides the subsidy. This means that miners are free to pick whatever transactions they like (as long as they are valid), regardless of fee. Due to block resource limitations (size pre-segwit, weight post-segwit, sigops, ...), the optimally rational choice tends to be to prefer transactions with high fee per weight. This effectively creates a block space market, where transaction creators bid for the rate-limited space available in blocks.
Some protocol rules on the public P2P network have additional rules for relay. For example, there is a minimum relay feerate (1 sat / vbyte), and replacement transactions have to &quot;pay&quot; some feerate for the bytes of the transactions they replace. Their minimum values are not set by the market, but by policies implemented by the network's node software. They can also be bypassed by submitted directly to miners. During times of contention, these rules are mostly irrelevant, as the markets will force transactions to pay higher feerates anyway.
A long time ago, the default mining software that came with the Bitcoin client included a policy that would reserve a small area per block for &quot;free transactions&quot;, which were selected based on &quot;priority&quot; (which was defined in function of age and value of the UTXOs spent rather than fee). I believe this was intended to promote cheap transaction usage. It was purely a client-side choice that was uneconomical for miners.