Populations of the towns on the route, mainline to Dover vs. diversion onto the Portsmouth Branch. . .
Atkinson - 7087
Plaistow - 7830
Newton - 4820
East Kingston - 2441
Exeter - 16,049
Newfields - 1769
Newmarket - 9430
---Portsmouth Branch---
Greenland - 4067
Portsmouth - 21,956
Durham - 15,490
Madbury - 1,918
Dover - 32,741
It's passing up twice the population strictly on the route, not counting places in the overall catchment like Rochester (32,492). Secondly, it's a long schedule via the Western Route making all the local stops. Boston-Dover took 1:52 in 1967 the last time there was MBTA service, and that was running nonstop on the NH Main before starting to pick up the local stops (Salem St., Ballardvale, Andover, Shawsheen, Lawrence, North Andover, Bradford, Haverhill, Atkinson, Plaistow, Newton Jct., Powwow River, East Kingston, Exeter, Newfields, Newmarket, Durham, Dover). To mount that today you wouldn't be able to repurpose a Haverhill local for super-extension as even with fewer NH stops (we'll assume that Atkinson, Powwow River, East Kingston, and Newfields aren't going to make any modern roster) you'd still be pushing 2 hours when all's said and done. You'd probably have to run that as a whole extra-layer MA super-express that hops Anderson-Woburn, Lawrence, and Haverhill...then starts going local with Plaistow, Newton Jct., Exeter, Newmarket, Durham, Dover in an effort to pound it all down to 90 minutes. Sort of how NHDOT studied out Concord as being a super-express layer on top of local Lowell-Nashua trains. Here that's not going to leave enough bandwidth on the Western Route with Downeasters and freights in the mix to tag-team a forked Portsmouth service of two schedules north of the border, because both forks would have to be run as super-expresses to achieve any kind of acceptable schedules.
Contrastingly, the 2001 Newburyport-Portsmouth study had an all-local trip doing extension stops at Seabrook (pop. 8401), Hampton (pop. 16,214), North Hampton (pop. 4538), and Portsmouth in 1:35 with plain-old diesels and Class 4 track. It's a very stark difference on schedule, ops ease (no change in frequencies to Newburyport required), and population served that a Western Route force-fit is woefully unable to approximate.
I think you could easily do a Dover super-express by its lonesome as that would beneficially boost service to Lawrence and Haverhill downtowns deservingly well above plain-old Regional Rail schedules, but Portsmouth is always going to have to run by the Eastern Route.