"if the hammerless boxlock had come first"
It did. The patent for the Anson-Deeley hammerless action dates from 1875, the Beesley action used by Purdey from 1880, the Round Action from 1881, and the Holland Royal was later still.
The Boxlock is the the older action, it is the watershed that shifted SXS design from lever cocking to barrel cocking, the principle on which all other "great" guns are based. All other SXS owe a lot to the lowly Boxlock.
The Round Action in my opinion is the best looking SXS ever built, but there is more to it than aesthetics. It combines the desired 90 degree sear to tumbler engagement, a solid bar, intercepting safeties in a package that is more compact than a sidelock.
Stocking is sensitive point in guns with grip screws. Stock bolted round actions, like the modern Chapuis prove that stocking can be as strong as any other double gun. The Chapuis can be counted a true round action as it has a trigger plate lock and rounded bar.
