While this doesn’t expressly address the “are there single traveler, pod-type hotels in the US?”, it does offer a solution that the pod-type hotel would – lower cost.
The cost of the hotel room in a particular city (in the US, at least) is dictated a couple of factors:
The “chain” or brand of hotel you’re booking.
Hilton is more expensive that Motel 6. Always and forever.
The location of the hotel.
Downtown is more expensive than the suburbs. Generally. Some suburbs have a large business sector and are more upscale than others.
The general concept is that business travelers aren’t paying for their own room, so they’re less cost sensitive (hey, the company’s paying, might as well have a nice place, right?), but they’re highly convenience sensitive (I don’t have time to travel from the work place to a cheap place in the ‘burbs, especially after wining & dining a potential client until late in the evening). Additionally, the business traveler may not have private transportation (a rental/hire car) and be fully dependent on public transport and/or simply walking from the work site to the hotel. (I was in that situation for a new job – working remote, but spent a week onsite to meet people – my hotel was literally across the street from the work site.)
However, individual travelers on vacation/visiting family/etc. are paying for their own room so they’re more price sensitive and less convenience sensitive.
If you need to visit NYC, consider staying across the river in NJ. Hotel rooms will be cheaper (even for the same brand) because location, location, location! You’ll pay for it, though, in additional travel time, cost and inconvenience in having to get in and out of the city each day you need to make the trip. This is exactly what my wife & I did when we visited my family in Manhattan with our young kids a decade or so ago. We stayed in Jersey and made an adventure of traveling into the city each day so it was fun for them. We took the tunnel, we took different bridges, etc. As a family on vacation, we could do that. As a business traveler, that would have been a nightmare.
Generally speaking, you’re going to get the same quality and amenities by choosing a suburb Hilton v a downtown Hilton (substitute Motel 6, if desired), but you’re going to pay less the further away from the city center you go.