These are things that keep me up at night, yes
However
Given that a) westerosi ecology is presumably adapted to the absolutely bullshit seasonality, and b) any area that size (possibly as much as THREE! THREE! times the size of motherfucking Scotland) is going to experience heterogeneous population densities, and therefore bits will occasionally have lower grazing pressure, c) there's not 'no new growth' because nothing's growing but because it's all getting eaten and finally d) the Kingswood soil is the kind of incredibly rich you would expect from a temperate rainforest,,,,, it is possible that you could get that many fucking deer-and-associated hanging out in there eating anything and everything that dares grow a leaf below browsing height. Not necessarily likely, I'll grant you, but frankly no less likely than anything else in westeros right now.
The main limits on primary productivity - vegetative growth - are a) light and b) water with c) warmth coming in a somewhat more distant third
The stormlands has all three of those in spades, so it can grow things at approximately the speed of light. I really cannot overstate how much greenery somewhere like that can generate, it's just that normally it'll hit maximum resource use and slow down as things start overshading each other and shit. In an environment where any new growth gets immediately eaten and then shat out as high volumes of - essentially - compost??? Yeah. So much.
While I suspect any ground plants that need to set seed to survive are in shorter supply, there are always seeds and whatnot coming on from outside Outliers Forest, and - as any gardener will tell you, at length and at high volume - there are always pioneer species (weeds) that seem to fuckin SPAWN whenever there's a clear patch of earth left unattended for more than about five seconds. The Kingswood seedbank might be beginning to run low, but ~gestures helplessly~ they can apparently happily reseed after a fuckin MULTI YEAR WINTER so I would not be taking any bets there 🙃
(what this seemingly inexhaustible supply of large herbivores is doing to the *rest* of westeros's ecology is another, differently horrifying thought experiment, although it does explain how Nymeria can collect a wolfpack ostensibly nearing or exceeding 100 without them just obliterating the Riverlands' ecology, since presumably there's basically infinite deer emigrating North from the Kingswood. There must be. So many predators outside the Kingswood. (None of this makes any sense, we're trying to apply logic and science to a world invented by someone who fundamentally Does Not Understand ecology or SCALE! A royal hunting reserve THE SIZE OF A COUNTRY?!?!) I'm amazed the wolves only became a problem once Nymeria got involved! Fuck knows what the VALE is doing, with their ludicrous geographic border defence. Westerosi ecology is just. Such Bullshit)
Deer tend not to debark old trees - it's too tough and dry for their needs/tastes - so any of the young trees they can debark have already been debarked, which is one of the reasons Garrit is going so feral: between the immediate consumption of new seedlings and the death of any existing saplings below a certain age, there's possibly upwards of a fifty year gap in tree age. Which is, as almost any forester will tell you, an absolute fucking disaster, even when you're not part of a society that depends on wood for everything from fuel to building supplies to shoemaking
The Kingswood foresters have been staring down absolute disaster as it barrels at them at full speed, fully aware that they or their descendants are going to be blamed for it when someone in power actually deigns to notice it, because never in history has 'we tried to tell you but you ignored us!' worked as an explanation on nobles like Tywin Fucking Lannister.
Forget the Seven, Garrit and co now worship Those Three What Fucking Believed Us from now until the heat death of the universe