I hate to tell you, but if you think you can transform the nursery industry, you might want to think again. I think what you're calling a "regular nursery" is a "plant retailer." Big Box stores have overtaken the industry and typically employ people with zero-to-scant knowledge of plants and sell rafts of product carefully coordinated with huge grower-corporations (think "Proven Winners" and the like) disseminated through marketing channels and trade-shows to develop a thirst for some new variety or cultivar in a seasonal blitzkrieg. Of course these big retailers will also carry a selection of bread-and-butter landscape palms: queens, kings, Washingtonia, Butia, Trachycarpus, et al depending on the dictated climate zone. They will likely special-order something if it's available from their regular list of suppliers, but the wholesale growers are also tuned in to what sells and grows quickly because they have to stay in business...and real estate, containers, soil and water are expensive when there's little hope for moving the plants out in good time. A production-to-market time of three years vs. seven years makes a huge difference in the profits of a grower, and as others have mentioned above, this is why you will find queens, kings and in particular Washingtonia over Sabal...they grow, and thus move, quickly. And Joe and Mary Homeowner are happy to see a nice fast-growing "palm tree" at their new tract home because they suffer from our modern-day need for instant gratification.
In SoCal it's almost a miracle that we now see Bismarckia sold regularly in garden centers; with Ravenea heavily pushed for the houseplant market. Yes, Foxtails, Triangles, and a very few others are occasionally encountered, and it took many years for this latter group to gain any kind of foothold, which is really not even a foothold, they're still oddities to many but they grow at a decent speed and growers can probably make a bit of money on them in certain areas. Sabal is not likely to join even that outlier group, despite its hardiness and other positive qualities, because it is just not a fast-growing palm and has no customer familiarity. It's just an uphill battle for both the grower and the larger retail channel.
While the rarer-and-rarer traditional nurseries will most likely order many plants from wholesalers, they are often growers themselves, they may go to great lengths to acquire propagation material of unusual species, nurse them, shift up to saleable sizes all by their own hand. They may buy bud-wood and graft fruit trees using a known rootstock for their area, etc. These are generally multi-generational, dedicated and knowledgeable nursery people whose horticultural and real-world experience in the landscape have gained them a major reputation and make for a completely different experience that appeals to serious gardeners who want to gain horticultural or botanical knowledge. Those nursery-people also gain a lot of satisfaction from interacting with customers and exchanging knowledge and experience. But they are realists, and if you get them into a conversation about something like Sabal, will likely say, "well, we don't get any call for them, so they're just not something we carry, and we can't even special order them without importing them from Florida, because they're just not profitable for growers here. You should go to a specialist palm nursery."
And here we lead back to the community of specialty growers, including backyard growers, who offer a wonderful array of plants that was unthinkable even fifty or sixty years ago. It is thanks to these people who have poured their hearts and wallets into a risky business that we have them...so I think the best thing you can do is spread the word to others about the palms you champion and point people in the direction of these knowledgeable and dedicated nurserymen and women who have enriched our personal and, for many, professional lives with a variety of unusual plants that was unthinkable a few decades ago.