This is understandable to think as a pax, and it possibly is possible, on occasion. However, I'm guessing its a lot more complicated for ops. Weather and conditions can change instantly and often.

When the plane took off, the estimated arrival time is given based on estimated conditions enroute and expected at the arrival city. Every time this changes, the inbound flight can be affected. If weather at the airport changes, this can mean the runway configurations change, amount of runways used can be changed, distance between aircraft might need to be lengthened, etc., meaning the aircraft could arrive later.

Not to even mention the aircraft from the departure before yours at the scheduled gate, which could be delayed and still sitting there because of conditions at your airport, or the destination airport of the flight. Which means your plane could arrive, and they either need to find another gate, or it has to wait for the aircraft there to leave. Then there's weather conditions enroute to your destination, which even if its good at the departure and arrival airports, could have an effect. Multiply this by all the other aircraft movements ops has to consider, many dealing with the same issues as your aircraft/listed above.

I'm sure there's a lot more to it, also (and no, I haven't worked in ops). Most paxs won't think about that. But its not so easy as UA saying, we want to leave in 20 minutes.