Since miners are also nodes at the same time, they should be capable of sending transactions. So the question is, can they mine their own transaction technically? And if yes, are they allowed to do do? If yes, a miner will surely have maximum advantage on his own transaction and he should be able to mine it with a success rate of 100% and way faster than any other miner on the network. This defeats the concept of consensus.
When a miner creates a block, he can put whatever transactions into that block that he likes, including his own1.
However, creating the block locally and populating it with transactions, and then successfully mining it, are two different things.
For the block to be mined it must contain a valid proof of work, which proves to the network that the node has solved a computationally difficult problem. The difficulty of this problem is in no way related to the transactions the miner has decided to put into the block. It isn't any easier to mine a block containing your own transactions - the difficulty comes from elsewhere.
1The current vanilla Geth code prioritises transactions in a certain way, but a miner can edit the code in any way he likes to prioritise things differently.
Even were there some advantage (as @Richard Horrocks points out there is not) there's no way to ban it. A miner can just send from a different address than their block's coinbase, and appear to the protocol to be a separate entity.
Note also that while it is "free" in a naive sense for a miner to mine their own transactions, it has an opportunity cost. Any gas they spend is not gas they could have had other users pay for. In that way, there is little benefit for a miner to mine their own transactions--they might as well just broadcast them normally and let anyone mine it.