I've lived in several places with HOAs, and they have all been good to great.
You say that you don't know if an HOA can stop the neighbor. That may be true, but they can force him to decide whether he wants to continue mowing HOA property and destroying plants paid for by the HOA, but also face a bill for replacing those plantings (and eventually fines if he refuses, which can become a lien on this property if it gets to that point).
That's generally the "teeth" of an HOA--fines. While some are nastly, generally it is "you have 30 days to remove the inoperable car from your front lawn. You can apply for an extension if you explain your son is coming on day 45 to tow it, but can't get here before then. After that, there are fines, which vary in amount and usually escalate. At some point when the amount is high enough, they can place a lien on the property. If they are good, they will work with someone on time, and also keep them informed of the steps to come so they can be avoided.
In a case involving violations of a common area that include destruction of property (and yes, destroying the landscaping is just that), they would likely bill for the damages. This might extend to liens if necessary (probably depends on local HOA laws, as well as your HOA rules) or even court.
When this guy is hit with a $500 bill for destruction of landscaping (after it is made clear that the HOA has decided on X landscaping in the common area), he may reconsider. Him mowing down landscaping he doesn't own is no different than if he did it in your yard, and the solutions available to the HOA are similar (actually, the HOA probably has more options). So while it may be true that you can't stop your neighbor from destroying your personal flower beds, it's unlikely he's going to keep doing it if you decide to use the means available to you to stop him.
But hopefully it won't come to that. When an HOA puts out a notice that they've decided to go with X plan from Acme landscaping and work will begin August 1, and that the area will be maintained by Acme) or the HOA landscaping committee in accordance with the Acme plan, or whatever, he most likely will realize he can't just change that at his own whim.
Also, the HOA can absolutely include in the by-laws that ATVs are not allowed on community property. That way, at least is his kid is hurt and he decides to sue, you have some proof you tried to stop it. And you might even be able to go after him to pay off the lawsuit since it was his violation that cause the injury, making him unlikely to essentially sue himself.