No there is nothing adverse about low monthly use, quite the opposite it means that the printer can handle the rating with the manufacturer expecting it will outlast its warranty. It means the printer will have a longer lifespan, and generally, cost less per page from larger toner carts.
Unlike ink, toner carts can work fine for years, possibly not in the most extremely humid environments but this would affect any size of printer.
I'm not suggesting to go high end for 1K pages a year, but I would go at least one step up from their sub-$150 models, adding a little more to that if it has the scanner or other extra features.
You might get more printer for the money buying used, say off craigslist.... just need to SEE it print before trusting the seller and if the print is a little speckled, most likely just means it is due for a new cartridge because owner bought a cheap generic last time.
On the other hand, that is the wrong choice for some people. Built in OS support for a printer is not adequate if it has extra features, so something too old, may not be supported by the manufacturer the next time you want to upgrade your OS.
IMO, you are better off buying OEM carts new and refilling with toner, than buying reman carts instead, because the reman carts tend to have low quality drums in them, or worn past what may be acceptable. On the other hand past a certain size monochrome printer, the drum is separate from the toner cart.