Boss and Co launched their o/u in 1909 and Woodward in 1913 - so about 100 years ago. I think it boils down to matter of preference. Today many shooting schools only has over and under - new guns will buy what they are taught to use on the range. Lack of demand for sxs means the makers will produce over and under - simple economics. Manufacturers are there make profit.

I shoot better with o/u even though I must admit a sxs might be nicer and more classic. For those who want a newly made sxs there are a few makers to choose from in the mid-price segment. AYA and other continental makers out competed the British boxlocks after ww2 as they could make less costly guns than British trade to market. Market segment left for the British makers were bespoke guns market segments competing, today competing with Bosis, Fabbri, Flli Rizzini and Piotti plus some others makers of great premium guns.
Even back in the days Boss & Co was considered to be too expensive for many with good financial means.

I find double triggers suitable for shotguns when barrels are choked differently. I had W-r sxs with selective single trigger and it worked fine. Boss single trigger is very complex and labour intensive to fix if there are issues.
Double rifles for dangerous game the double trigger choice is better as the hunter has the instant opportunity to select soft or solid. That is what I would get for dangerous game hunting

Sxs doubles recoil differently than o/u and shallower opening angle to reload both chambers. Between 1960-1990 there was a very limited demand for big bore sxs doubles as classic safari destinations closed or restricted hunting - 375 H&H and 458 win mag were about the only two caliber you could find factory ammo for.

If you fancy very high driven pheasants many will go for 32 inch barrels, 34-56 gram loads no 5 or 4’s and tight chokes. A classic sxs game gun 29 inch barrel, Imp cyl and 1/2 choke may not be what most choose for the task. People in the industry says the demand for sxs has increased again.