The Acheron as a Yankee built frigate is implied to be at least inspired by the Original 6 Frigates of the US Navy designed by Philadelphia Shipwright Joshua Humphreys. Its more on the nose in the book the movie is based on, as its and actual American frigate that provides the main antagonist. The Original 6 were broadly of 2 types, the Super Frigate +44 gun larger hulls, and the slightly more conventionally sized 36ish gun hulls, which is closer to what we see in film and IIRC is depicted in the book.

Humphrey's favored designs that were both longer and wider, and sat lower in the water, this made them fast and stable(there is a bunch of math to it, but generally the longer a ships length at the waterline the faster she will be all other factors being equal), but also meant that had to be generally larger to begin with. Meaning ships were more costly and long to build, and required more crew, and would be more costly to maintain on foreign station or extended cruises. Which would all be issues for a Royal Navy that needed hulls in the water, doing Navy things, in lots of places at once during the era. There was also a greater institutional willingness in the new US Navy to overload their ships with more and heavier guns than an equivalently sized British ship, for good and ill, but often in both forces what was available when fitting out or during construction was the overriding factor.

Humphrey's also insisted on the harvesting of expensive and costly Live Oak from Southern Coastal swamps for use in what amounts to the 'ribs' of the Original 6. This wood was extremely strong, brutally difficult to get(and the process would see dozen's of workers dead from disease, many of them enslaved Africans), hard to work with, but would hold up well, and gave the ships an exceptionally strong frame. This also could be used to help the hull maintain its shape, along with diagonal braces in the design. Hogging, or the sagging of the bow and stern of the hull would degrade the sailing characteristics of the ship as well.

So the American heavy frigate design was very much a product of a gifted, maybe a little eccentric Quaker coming up with a design using US sourced materials that were for a ship that would almost always be outnumbered by potential foes. Meanwhile the Admiralty was trying to procure, man, and run a global navy and that doesnt always mean building the biggest, most heavily armed ship you can of each type.

Hope this helps! Let me know if you there is anything I missed you were still curious about!