Alright, so the idea is that insulin is a growth agent, and too much of it will cause too much growth, and that growth is mostly horizontal. Let's use growth hormone for comparison to see if it's actually growth we're seeing with insulin. Their overall action is different.

Insulin. Normally regulates fuel systems primarily, and protein synthesis and enzyme production and so forth secondarily. Don't need much of it for that. Too much will first disrupt these systems, resulting in growth of these mechanisms rather than normal growth otherwise. With normal insulin, there is no growth to speak of. Instead it's more of a normal balance of stuff going in and out of these tissues, so fat and glycogen and protein and enzymes, etc. Some tissues will actually grow from the action of insulin, like fat tissue for example which will grow permanently in a process called insulin-induced lipohypertrophy, this needs chronic hyperinsulinemia.

Growth hormone. Normally causes growth, rather than regulate it. Though if we see it as regulation, not enough of it will stunt growth, too much will cause excess growth. The tissues that grow from GH are generally different from those that respond to insulin. Mostly it's all lean tissues. This growth is typically permanent as well, but there's normally very little growth and it's in the context of repair and maintenance when past puberty. Since GH causes muscle growth, there is some horizontal growth as well, obviously, but it's just as obvious that this growth is more health-giving than otherwise.

Insulin and GH are directly linked by diet - carbs - through the inhibitory action of hyperglycemia on GH. Too much carbs ==>> GH inhibition. Between insulin and GH, GH is the most potent growth agent for basically all tissues. On the other hand, insulin is the most potent growth agent for things we don't want to grow - fat tissue, cancer. In a general sense, growth occurs between meals, i.e. while we sleep for example, GH does its thing; insulin, when it's too high, disrupts Ein-Eout at the fat tissue which results in less fat coming out - net result is excess fat accumulation in the short term, insulin-induced lipohypertrophy in the long term.

Insulin and GH are also directly linked by growth itself. When GH says "grow", insulin is bypassed by other hormones and enzymes to release more fuel for this growth. When insulin is too high, there's no bypass or very little, so little growth. But then when insulin is too high, usually it's because there's too much carbs, so GH itself will be influenced before it can even say "grow". But let's imagine GH responds normally, it's not inhibited by hyperglycemia. Insulin is too high, doesn't allow enough fuel for growth, GH becomes basically useless. We could even imagine that since insulin acts as a growth agent for things that we don't want to grow, but GH is still the most potent growth agent for everything, now we have two growth agents for things we don't want to grow instead of just the one - insulin + GH, instead of just insulin.

So, is it actually growth? Yes, to some extent, but only for a few specific tissues, while all other tissues don't grow, in fact they shrink due to lack of GH from the hyperglycemia (if the main culprit is a high-carb diet). Think of it as a car where the gas tank grows too big. It's not actually growth, it's just the fuel systems that are disrupted in such a way as to accumulate too much fuel primarily, and generally grow bigger to accomodate this excess fuel, while the engine sputters because it's not getting enough fuel (the primary mechanism by which that gas tank grows larger). And this abnormal growth is not necessarily growth as we understand it, rather it's a side effect of the disruption of the systems that do grow. For this, imagine garbage collectors go on strike. Well, garbage will accumulate right on the sidewalk, but not as a first thing, instead it's a by-product of lack of garbage trucks, see?

As a side note, my paradigm says there's a normal balance of fuel substrates - glucose and ketones primarily. This balance is directly linked to insulin level in a three-way. When glucose rises, insulin rises, ketones drop. When glucose drops, insulin drops, ketones rise. See how both glucose and insulin rise and drop together, while ketones opposes them. At first we understand it from the point of view of diet, right? But when we inject ketones directly, ketones rise (obviously), then both glucose and insulin drop. I believe this balance is essential for normal cell function, so when this balance is disrupted (especially by a high-carb diet, and especially when ketogenesis is shut down by too much insulin), all cells can't work properly, this also means the fuel systems and the growth systems. So, normal growth is less than otherwise, while abnormal growth (growth that can occur even if or because those systems are disrupted) occurs more than otherwise. A sort of favorable environment, if you want.