I thought of that idea many years ago, I even constructed a working model of an engine that could work with compressed air, alternately it could also burn hydrogen, giving it much more power.
Never did get further than the testing stages of the engines operation.

Once the initial 52-gallon fill has been emptied, the CAT can be recharged in two different ways. If there’s a nearby electrical outlet, the car can be hooked up to a local electrical grid, and with its onboard compressor will fill the tank in about four hours. This method costs about $2 or so in electricity per tank, which makes it the cheapest vehicle to fill we know of. The second way involves hooking the car up to a compressed air station, such as the type found at gas stations. If you can find the air for free (becoming a rarity), then there’s no cost to filling up. It also only takes two or three minutes, making it a more convenient solution.