About the wallet, for example online wallets like blockchain.info, they can control the fee amount to 'help' miners?
Actually talking about blockchain like wallets they have enabled fee recommendation system which calculate the optimum fee to get your transaction included within next block. So actually they are not helping miners, they are helping users so that transactions doesn't get stuck for several blocks. To obtain optimum fee for each byte of transaction in real time
https://bitcoinfees.21.co/ provide helpful tool.