I kind-of agree and kind-of disagree with this logic, with the biggest things being how do we compare this both in-game and in-reality to other edge cases?
To start, I do technically lump the Scharnhorst into the German WWI-BC genre on account of its inability to fight *most* other proper battleships in a fight (had they not fought Britain, they would have been effective against everything shy of the Richelieu for France or Russia). That said, Germany is the only nation that ever built that style of light battleship, so it gets a little weird when comparing them to other nations.
In game terms, the Scharnhorst being treated as a battlecruiser is wrong; if the metric used to downgrade it from a battleship are its guns, those don't impact its in-game definition--the armor does. And the armor is definitely battleship grade. Engine speed also doesn't really have any BC/BB rules after WWI, with battleship engines varying by over 100,000 shp (more than the total weight of some BC engines). If Scharnhorst, Bismarck, Richelieu, Littorio, and Yamato
all fail to meet historic speed capabilities, then they probably need a faster engine (I'm in favor of those nations starting with BB-engine 3, among numerous added naval techs across the board). Moreover, the Iowa class would define as a battlecruiser if speed and hull were used to define it rather than protection first, with the ship having a slightly-thinner armor belt than the Scharnhorst and a relatively-narrow beam to allow passage through the Panama canal (plus its very high speed). As a random note as well, despite having a large engine by battleship terms, Scharnhorst's engine is about the same size as the Trento-class heavy cruiser's engine (150,000 shp).
As for reality, it's important to remember that while the limited capabilities of Scharnhorst's guns might drop their actual performance down from battleships, a few keys do need to be noted as exceptions:
- It's hullform is still battleship-like (this isn't a long, narrow hull built for speed over survivability like other battlecruisers or narrow fast battleships).
- Italy's 4 dreadnought refits would downgrade to battlecruiser if capabilities were used to define them rather than design (they are underarmored compared to any fast battleship, and their guns are only 320mm). By comparison, most other toss-ups are originally-built as battlecruisers (or clearly follow BC specs, like Dunkerque). A bunch of dreadnought designs even compete with battlecruisers for protection (the España-class being the most egregious, with a 305mm 6-8 gun broadside and 8 inches of belt armor).
- If another battleship was present (i.e. Tirpitz), the Scharnhorsts could have fought in the line of battle despite being undergunned. The same couldn't really be said for battlecruisers like the Renown or Kongo, which couldn't take hits from large battleship guns. These ships only used their 28cm guns because those were all that could be easily-produced (especially since they were already in production) by Weimar Germany compared to several larger gun plans.
One last note, regarding a refit of the Bismarck's guns I think that may be an error, the Bismarck had 4 twin turrets, not 3 triples (so they couldn't swap for wider twin barrels). Boring the guns out could bring up their width, but I'm not familiar with any work done to test the feasibility of this (due to weakening the barrel, plus whether the ammo hoist could support the new ammo). The 406mm guns for the H-39 were considered feasible to bore out to 420mm, but it probably helped that the ships hadn't been built when that design change was proposed for the H-41 (no actual ship work) and the guns were described as oversized.