Most shotguns are used primarily as hunting weapons. The game is nearly always moving, usually as fast as it can, and quite often airborne. The motion required to operate a pump doesn't disturb the tracking of and pointing at such targets nearly as much as does that for a lever action. While the same does hold true for rifles, it has become less relevant in the field as the ways that folks usually hunted deer and small game changed.
Sadly, relatively few folks that I know still routinely use a rifle for taking rabbits or squirrels anymore. The countryside around here is generally pretty 'flat' and open and it has become much more 'developed', for one thing. Many of those who pursue the tasty tree rat seem to lack the time or the patience to stalk them and wait until they're stationary to take their shot. The fact that for many years now the only legal arm for deer hunting during the regular 'Firearms' season has been a shotgun might have something to do with it, too, but that's just a personal speculation.
The main reasons that the Marlin and Winchester LA .410s weren't exactly stellar sellers, IMHO, are: that they were more expensive compared to most other .410 repeaters, they wouldn't cycle 3" cartridges, and they offered no significant practical advantages afield for the extra cash.
Up until relatively recent times, most all LA and pump rifles were exclusively chambered for what are now considered to be low-to-medium powered cartridges. As the paradigm for what constituted 'high' power in a hunting cartridge shifted towards the .30-06 after WWI, and more Americans became familiar with the BA rifle's capabilities, tastes began to change. For many years, the .30-30 and cartridges of similar ballistics were still considered to be perfectly adequate, if not ideal, for deer and similar game and the continued to be popular. After WWII, when surplus BAs in more potent chamberings became available at rock-bottom prices and advances in the manufacture of optical sights made scopes tougher, clearer, and much less expensive, the ranges at which game could taken humanely and reliably started to change the definiton of what the average 'deer rifle' should be radically.
There were pumps like the Remington 76, LAs like the Winchester 88, Savage 99, and Sako Finnwolf, semi-autos like the Browning BAR and Remington 74 introduced to compete with the BAs on their own terms, and some of them are still around. But they were never perceived by the largest portion of the market as having comparable potential for precision accuracy to a BA, or enough other practical advantages to justify their sometimes considerable extra cost.
As a southpaw, I gravitated to pumps and levers early, as they were the only repeaters that I could get that were both available and affordable. My favorite small game/woods-bumming carbine is an IMI Timberwolf .357 and I wouldn't trade it for diamonds. I hunt deer with a Savage 99F, a Marlin 336 in .35 remington, and a Marlin 1895G in .45-70, as well as my LH Remington 870. My nephews' favorite plinkers when I take them to the club are my Rossi M62s and little M92 'Trapper' .357. Like tuner said, why should I buy a BA just because it's different?