I would avoid using:

AmbiguityFunction -> First

When you do that, you're essentially asking Wolfram|Alpha to provide a complete list of all possible people that name. The "First" is then ran later, so it's a bit of a waste. The default value of the option, Automatic, gives you the most likely interpretation.

Also, AmbiguityFunction is just a very confusing option overall. "First" doesn't really give you the first value from the AmbiguityList. You really have to use a ReplaceAll and some pattern matching to work with them as some of the documentation examples show. It's unintuitive.

I did a bit of digging. I would expect that both

Interpreter["Person"]

and

Interpreter["Person", True &, Missing]

Would do the same query to Wolfram|Alpha. And they do. After all, the second one really just says what to do with failing interpretations. One interesting thing is that this query might request the PersonData paclet the first time it's called, which would make it take longer. Subsequent evaluations don't seem to call Wolfram|Alpha because the data is cached.

I could imagine that it might make sense to preload PersonData by calling it in some cases, but I don't think that's actually really helpful to you. I don't know of a workaround really. We could write some code to locally try to associate a String to one of the president entities. For a case of this size, I think that's feasible.