It's an interesting thought experiment but there are a few problems.
According to general relativity it doesn't matter the compactness of the central body. Objects orbit a black hole the same way they orbit an equal mass star provided the distances are the same. From a distance there should be no change as the central body gets more compact.
General relativity correctly predicted gravity waves, light curvature around the sun, the Schwarzschild radius of black holes, gravitational time dilation and Mercury's orbital hick-up, so it scores a lot of points for making correct predictions and general relativity says your argument isn't how spacetime works. Granted, general relativity doesn't explain dark energy but so far, it explains gravity very well.
Stretching and expending space the way you suggest would imply that gravity creates more space between objects, which is not what we observe. To put that another way, if it creates dark energy expansion between galaxies, who wouldn't it create expansion of objects orbiting much closer to the black hole?
Granted, we've never observed orbits around black hole up close, but your theory goes against both the consensus and observations. Orbits appear to follow Einstein's and Newton's laws pretty much exactly. There's evidence of gravitational perturbations (Mercury's orbit) but no evidence of gravitational stretching space to create greater distances between objects.
A 2nd problem is that dark energy seems too be evenly spread not bunched around galaxies. The black holes in the observable universe are somewhat structured by into clusters and superclusters. Dark energy doesn't appear to share that kind of cluster structure. The WFIRST Telescope, due to launch in 2024 should get a better image of dark energy, do it might shed some light on this.
A 3rd problem is that dark energy is the most abundant thing in the universe. Black holes, even supermassive ones, are just a small percentage of galactic mass, so it's difficult to explain why the relatively local and comparatively small mass of black holes would generate so much dark energy, greater than all the mass of all the galaxies and dark energy combined.
That's just my take. Feel free to read it with a grain of salt.
Could gravity drag or stretch space? Well, maybe yes. Gravity probe B found that rotating massive bodies drag space around with them, so maybe space can be stretched a little. This is called frame-dragging.
But these effects of stretched space, lets include general relativity predicted gravity waves and frame dragging are very small and very local. It's hard to explain why they would affect the expansion of space across millions and billions of light years.
A final problem that I feel is worth mentioning, is that physicists don't know what gravity is. They know how it behaves, but only have untestible hypothesis of what it is.
They think it's probably a very very low mass, very hard to detect, spin two particle called a graviton, that's so weak that it may be impossible to detect.
Physicists also don't know what dark energy is, so, if your theory is that this one thing - which physicists don't understand, is tied to this 2nd thing - which physicists don't understand. That's going down the rabbit hole of unpredictability and un-testability pretty far.
Many of the ideas in quantum physics are successful because they've made incredibly accurate predictions. The ideas may seem highly counter intuitive but the predictability makes a lot of it a valid theory. We have no theory of gravity and no theory of dark energy, just ideas that may or may not be accurate.
Good physics requires testability and repeatability, or at minimum, a very convincing set of equations. Gravity and Dark energy are on the outskirts of that, in the realm of the unknown.
Please don't mistake my "this problem/that problem" answer as dismissal, because I think yours is a cool idea that a black hole could stretch space and maybe it can, but it's a tough sell, because dark energy appears to be everywhere, and there's so much of it and there probably weren't always black holes, they presumably came later, after the first stars, which came well after the cosmic microwave background radiation, which came well after expansion. Just my 2 cents.