Something not mentioned in the other answers, and which your question implies you are unaware of, is that there is no requirement that one have any transactions at all. If you want to mine a block that consists of nothing except you getting the block reward, that is a perfectly valid block. This is something that has happened, although it was more common in the early days.
The reason it usually doesn't happen is that transactions generally have a transaction fee. This is where the person sending bitcoins includes in the transaction that the person who creates the block with the transaction in it gets a portion of the sent bitcoin. This isn't mandatory, but obviously it creates an incentive for people to include your transaction. If you were to create a block consisting only of transactions between your own wallets, then you wouldn't get any transaction fees (even if the transactions included fees, the fees would be paid from yourself to yourself, so no net benefit).
So what you're proposing would provide no benefit over just publishing an empty block (unless you wanted to make tracing bitcoin more complicated or something), and publishing an empty block is in turn worse than publishing a block with transactions that have transaction fees (unless you're trying to create a fork or something).
This way miners could make bitcoins for themselves out of thin air.
Yes ... that's what "mining" means. When someone mines a block, they get a block reward. Perhaps you mean "this way miners can get bitcoins without providing any benefit to the network". As I've explained, this is already possible with empty blocks (although I suppose one could argue that empty blocks still provide benefits to the network: for instance, by having more blocks after the blocks that do have transactions, those transactions are more secure).