if a delegate decided to require a higher fee for transactions to be included that only results in the tx to be included by another delgate at a later time .. so basically at a 10 seconds extra delay.
worst case 100*10sec delays if the 'cheapest' delegate is to include your transaction with your tx fee.
Further, the delegate pay is a average over all income. So if you decide to double your required fee for the delegate you effectively increase the income of all delegates by 2/101 .. the drawback is possibly a loss in confidence for your delegate