Boyfriend and I debate on sauteing noodles in pot or pan

Adding onto creamtea's excellent summary, there are a couple of notes.

In a restaurant, the pasta would be pulled out of the cooking water which would be reused for cooking additional portions of pasta because it takes too long to boil a fresh pot of water each time someone orders noodles.

Restaurants use something like this:

https://www.amazon.com/Update-International-APSA-4-Aluminum-Inserts/dp/B000X1QKQY/

so they can keep noodles cooking pretty continuously.

At home, I don't use anything like this however I frequently want to keep the pasta cooking water for other uses, like cooking vegetables.

Hot water -- even with a little noodle starch -- is still very handy and a more responsible use of a precious resource (at least here in drought-stricken California) for those who care.

It's probably more "correct" to sauté them in a wider sauté pan but then you'd have an extra pan to wash. You'd have more square-inch-age to fry them in and the moisture will be able to better evaporate and some parts of the noodles crisp up better. The added ingredients won't steam that way. I would understand not wanting to wash another pot though and after a long day I might opt to use just one pot too.