That doesn't really answer the debate why should magic be involuntary but responses to some skills be strictly voluntary, particularly if both uses involve overcoming the target's defenses.
The 'why' is "so that magic will be strictly superior." But that just begs the question. ;P The reasons 'why' a non-magical effect should be allowed to work mechanically are clear: game balance, fairness, consistency, keeping resolution character-focused (even 'realism' from that angle). It's just that no amount of valid game-design reasons can overcome a preference for caster supremacy. For a fairly large proportion of the fanbase, being a fantasy game means ready access to magic, and 'magic' means 'just flatly better than not-magic, no exceptions.' It's not a complicated position, nor is it entirely unintuitive - we know that magic blithely breaks physical laws. We know that technology accomplishes a lot just by following physical laws, so breaking them should let you do literally anything. Conversely, we know how limited medieval technology is compared to modern and how limited human capacity is without technology. So it's almost inescapable to conclude that there must be a vast gulf between what medieval-tech-using mundane characters can do and what magic-users can do, and it only makes sense for the latter to be strictly superior in every imaginable way.
Of course, if you look at the fantasy genre, that's not what's happening. The characters who use magic are there for support and exposition, and the heroes aren't using magic. Magic can't be depended upon (except to advance the plot), and it's very limited in what it actually does (often for no clear reason) and whether it can work in the face of little, very human, things like courage or True Love or Faith.
That seems... odd to me. I can't put my finger on it, because it's either so vague that any situation can eventually arrive at a player decision that precipitated it (up to and including sitting down at the table to play), or it implies that NPCs should always be reactive to player actions -- they can intimidate a PC, sure, but only if the PC puts themselves into a position for the NPC to intimidate them.
More the former, I think. Again, sorry if that's not too deeply insightful or interesting. I'm just trying to map the issue to the system.
When a player attempts intimidation, the system is clear: the DM decides whether the target is intimidated or not or he calls for an intimidate check. When an NPC might intimidate a PC, it's less clear. The action that precipitated the intimidate should come into it somehow.
For example, in a recent game, an NPC organization set out to intimidate a player character... So, was that a PC initiated confrontation, because the PC did something that caused an unseen and unknowable (at the time) sequence of events that led to the intimidation attempt?
Probably not.

That's a fairly complex set of things going on, rather than a single resolution.
Yet you seemed to be keen on making a statement that only some things are allowable -- that NPCs shouldn't initiate action, be merely reactive.
When it comes to a specific resolution, yes. But, the point is just that a check will likely only come into it when the PCs initiate something, the rest is just presented by the DM as the PCs interact with his world. So if NPC thugs stop by and harass NPC non-combatants the PC cares about, there's no resolution, the DM just has the victims relate the experience to the PC the first chance they get. That doesn't call for an intimidate check, either vs the NPC (the DM just decides how they react), nor the PC (who wasn't present to be intimidated).
The way I'd think about it is that Intimidate is a CHA check, so it's something you'd use to resolve an interaction. An indirect interaction, like a 'pattern of intimidation' - vandalism, scaring people close to you, leaving severed horse's heads laying about, &c - wouldn't have anything to do with CHA nor even be based on a single NPC's check. It'd just have to play out, because the game has no mechanisms for the whole conflict, the way it has initiative, hps, and the like to resolve a battle as a whole as well as rolls to resolve whether the individual attacks hit or not.
Imagine trying to run a D&D combat without initiative, turns, damage, hps, or conditions, using /just/ attack rolls 'contested' by other attack rolls (not even any AC).
That's the kind challenge presented by trying to use the extant skill system to resolve a complex interaction-based conflict like the one you describe.
I don't know, perhaps I'm overthinking this. I appreciate that you're responses aren't full of 'my way is better' and that you seem genuinely interested in engaging the topic. Thanks for the responses.
It quickly goes from a simple resolution schema to very complex issues, so, no I don't think you're overthinking it, it's worth this kind of examination if it helps us run better games.