(Seems more like a "Weeding" zone. It's not exactly using the full powers of Capability Brown.)
I think it sounds like an expansion to agriculture, once "constructed" farm-plots are changed to Zone-style operation.
You should have farmer-assigned jobs of systemaically tilling and seeding of any actively cultivatable crops, but also have option to either remove or nurture anything that self-seeds (including grasses, perhaps to bring in the Pasture functionality, or to feed by proxy with sileage). Farming is very very easy, as is, with only very understaffed fields (vs productuon capacity) suffering from crop-rot after harvest or suboptimal seeding beforehand. I don't even bother to use fertiliser, it just works (unless I neglect setting it up, due to other workl.
Adding in a sensible default, that you can dial up or down, of various tending tasks such as ground preparation (between harvests, as well as in setup), seeding, weeding, tending, harvesting and perhaps digging hack in. Fertiliser and other additional substances, like straw under strawberries or certain plant extracts to reduce pest damage, fit in there.
Possibly, with 'ground memory' you can suffer from over-farming into an eventual dustbowl or use crop rotation to improve the main harvest crop. Though this may mean a huge glut of extra tile data unless you accept a basic clay<->loam<->sand transition chance given the treatment of a tile, and keep it mostly within current tile-defining data structures (or restrict the 'memory' to just all tiles in a zone, but that begs for easy resetting by unzone/rezone).
On the crux of your idea, yes, this would support the interventions needed to prevent saplings, or to stop other plants popping up (maybe you'd select to allow wild carrots but not other things, if that's something you want - though you still couldn't get off-biome/tile-incompatible spontaneous crops just by 'allowing' them). I imagine(?) you want this feature as a better way of keeping wagon avenues open and/or preventing awkward and unnecessary vegetation on/above other current and future groundworks, rather than the road/stockpile methods. Just riffing on this a bit more, I hope you don't mind.
(@FD, you ninja you: I had considered "Get off my laaarnd!" enforcement, also, especially when subsuming pastures to be used only by allocated creatures, but you put it better than the thing I cut.
)
(@towerator, a further ninja: Yeah, hadn't gone onto that, yet, but logical. Assuming a dwarf can appreciate an outdoors park/it can be done with underground plant-zones. A biological statue-park.)