"block depth" does not consume computation power but adding blocks that include your transaction in blockchain does. what you are referring to is "mining".

The bitcoin network is maintained because of the capabilities of miners in securing the whole network by solving complex mathematical algorithms (guesswork). By doing so, miners are being rewarded of 6.25 BTC (as of now) in which they can use to sustain their equipment and to profit as well. Moreover, the transaction fees also helps in maintaing the bitcoin network if however the maximum supply of bitcoin has been mined.