Is that why US service ("checking on the customer every few minutes") is so incredibly annoying...

It seems like the universal standard in my area is that the server plunks down my food dishes and immediately asks if I would like anything else with that. And I don't know about neurotypical patrons, but in my mind it is impossible for me to process whether I will need anything else while the server is standing right there, staring at me and waiting for me to answer. So invariably I am forced to say "no" and then, more often than not, I belatedly discover what it is that my meal also needed, and so I wait to flag them down again (this necessarily involves not picking up utensils and not eating anything, so that they notice there is something amiss.)

I really haven't been smothered by checkups every few minutes. When the servers are really good, they can anticipate when you need something by simply looking at you and your table. They know when your drink is empty and when you want it filled. A server should rarely need to ask that stuff verbally. If they are continually checking up, they are inexperienced or insecure.

After I make my order, the server will usually try and take my menu. Lately I've said "I'd like to hold on to this" and they love when you do that! I don't always follow-up with another order, but sometimes I just need an extra side dish, or a dessert.

I've had that overstaffed experience, too. There are one or two small chains around here that employ 3x as many servers as they need. And their rooms are always 1/5th full or less. So the moment I walk in, there are 3-4 people greeting me and escorting me to a table, before I can even pull off my hat and gloves. In the same place, while they don't appear to do "team service" I would meet one waitress, and then get fobbed off on another guy for no stated reason. If they are sharing tips, a lot of slices to that pie.

No. After you've ordered, it is rare to order anything else. You might ask for a refill of a beverage or something like ketchup, but the waiter is not expecting more ordering. It's simply expected by diners that their waiter is there and will help with whatever they need. In Europe you'll wait 20 minutes to get the attention of a waiter for salt or ketchup until your food is cold. Also in Europe this will be described not as dead time waiting for a small thing, but as culture. European culture.