The Constitution places a few limitations on who can be President. One of these is that you must be a natural-born US citizen.
I wonder if changing the constitution will cost him less than buying Twitter.
I don't think so at all. The system is designed so that the American people, in the framework of the system, make it run. There's no need to worry that we only got the 2nd best person in the job, because we're not counting on their excellence to work miracles for us.
While on the other side of the coin, it's still possible for a bad actor in that position to wreak a lot of damage (especially given the historical erosion of controls on government action and the gradual abdication of Congressional oversight).
So it's more important to avert a potential disaster, then to avoid the cost of missing our one potential savior.
Let me ask you: would you go even a step farther? Should we allow non-citizens to hold the office? If not, why not?