Is the form “Mr. President” correct? We don’t say “Mr. Professor” or “Mr. Doctor”. Souldn’t the same apply to “President”?
The convention is to address high government officials acknowledging their titles. One would address the Secretary of Transportation as Mr. Secretary. I think, but could be wrong, that this only applies to Cabinet level posts or higher.
It’s a matter of style, not grammar.
“Mr.” is a variant on “Master”, which is an honorific. We are not consistent on who we apply it to, but there is no rule which says we have to be. The head of the executive branch is “Mr President” but the head of the judicial branch is “Chief Justice”. “Mr Chief Justice” is just one word too long, I guess.
At state level, the Secretary of State of (say) Delaware is “Mr Secretary”, but his boss is just plain “Governor”. Some way further down the governmental food chain we find “Mr Mayor”.
In the UK, nobody in the legislative/executive branches is “Mr” anything, but High Court judges are “Mr Justice So-and-so”.
And, of course, in both countries practically every adult male is, for social purposes, “Mr”.
Looks pretty random to me.
My understanding is that it originated from John Adams. He had a long argument with Jefferson on the correct way to adress a President, seeing as there was no historical precident in the English language for an elected head of state. Jefferson wanted the adress to be “Your Excellency” or someting similar, but to Adams this seemed too aristocratic for the “first among equals”, and he advocated instead the most modest form of adress he could think of: the basic job description with the egalitarian honorific of “Mr.”
Vice President John Adams, after being referred to in the press as “His Rotundity”, spearheaded a Senate committe to come up with some decent titles for the government high holies.