At least in America, whenever I go to a restaurant, the host or hostess usually takes the first turn in the conversation by asking how many people are eating with me. Why!?

About 95% of the time, the answer is obvious: Can't you count? There are two people standing in front of you?

Admittedly, it's useful information. But why not take a guess?
"Welcome! Two of you this evening? Please, follow me."

Does anyone else find this weird or have any thoughts on why it is basically a rule for all restaurants everywhere? (Even if you think it's silly, as I do, it would seem a little rude if someone decided to skip that social obligation!)

That's perfectly reasonable, but I don't get the impression it's actually (usually) due to need or uncertainty. That's the part that I find weird-- it seems grammatically (eg, conventionally) required to ask this question even if it's completely obvious. It's gone from practical to conventional, which interests me.

In contrast, many restaurants offer a carry out option, but a parallel question is rarely asked by default about that. And certainly it's hard to guess if someone wants to dine in or carry out just from appearances:
"How many this evening?"
"Oh, we'll just take it to go, thanks."

I think that's right-- it's somehow conventionalized into the formal greeting at sit-down restaurants. Language is weird!

Sure, but why not "2 this evening?" Instead of acting like it's impolite to even imagine guessing? Sometimes they do do that. But it's relatively rare.

The only thing I can think of is that asking a question places a demand on another to think which probably reduces their focus.

If you take a guess, you have invited someone someone to use your resources further.

So, I'll ask you, are managers conditioning these people or are they learning their behaviors elsewhere?