I think a combination of the two works - some with hard checks, others that are purely dice roll, some dice rolls that require a threshold to even engage with, some where both CHA and Speech are taken into account, some with just Speech, some just CHA, and some in combination with other skills, though this last category would probably be the rarest.
I believe that Planescape did this; IIRC, there were encounter checks that required minimum stat values to succeed. Fallout 2 had this in the encounter where the PC chooses the brain for Skynet. IIRC the quality of mind the PC chooses is based on the level of their Science skill.
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Here is how I see it:
PnP-RPGs and cRPGs both need to account for the very complex circumstance that can arise in its presented situations. This needs to be done impartially. The mechanical task of an RPG is actually to say 'No' in the "Let's Pretend" adventure whenever the answer should be No instead of Yes. So... can the PC lift the log?...No. Did the PC's attempt to defend themselves work as hoped?...No. Can they read the foreign writing?...No. The answer won't always be No, of course. Did the coin toss land Heads up?...Yes. Is the safe locked?... No—which is a kind of a Yes.
A computer could be made to track —everything—. An NPC could forget to lock their safe when they leave the house, and so it would be unlocked when the player chanced to pull on the latch.
An NPC could rob other NPCs, and suppose they jammed a lock during the break in—the lock would be jammed when the player eventually tried to pick it—making it impossible. Of course the player doesn't know this happened; how could they?
This is A LOT of stored variables across a gameworld; most of it never used. A human Dungeonmaster could not keep these kind of updated notes; a computer could, but it would be a lot of work to create, and be a lot of complexity to debug. So back to the point... RPGs must simulate impartial chance & circumstance, and an easier way to do that is through abstraction. Dice can be used as an impartial indication of chance & circumstance; whatever the roll is, it can virtually represent every—theoretical— thing related to the difficulty (or lack of it) in the situation at hand.
At it's simplest, the 50/50 chance of a yes or no answer. Can they climb it? Can they hear anything? Is it infected? Is this bauble worthless? Do I remember my French language training enough to puzzle out this note? The dice roll indicates an impartial sum of all of the [hypothetical] circumstances, to arrive at an impartial answer. Failure could mean
any possible reason for them not to succeed; slipping on the climb, wax in their ear, the toilet was used by a most virulent previous occupant' the bauble is platinum—so "it's not real gold", says the pawn broker.
In the case of skill checks it is not always a 50/50 chance, it's usually whatever the PC's skill level happens to be at the time. It works. The novice might succeed 20% of the time, while the expert might average 80% success; and they can both fail—or sometimes succeed by fluke.
An absolute expert (highest level) thief character can still drop the lock pick; failing the 99% skill check.
The common question is, "But if I can just roll again and again until success... then why bother with dice?". The answer is Time. The value of skill is the ability to do it accurately on demand. Anyone can know any fact if given unlimited time to learn about it, but the expert knows that fact in the very moment that it's needed. Anyone can pick a lock with unlimited time, but only an expert can enter a locked police box before the officer walks around it; back to the door.
An issue that is sometimes brought up against success by fluke, is that the PC is simply not skilled enough to succeed in certain situations. Consider a security door that cannot be bashed, and has a specialized lock, designed to be almost unpickable. A novice would never succeed by chance alone, and an expert would be hard pressed to manage it. Consider also, an NPC who not only doesn't like the PC, but who is in a foul mood to begin with. It would take a silver tongued car salesman to convince them of anything. In both cases would be uncommonly difficult.
This is where skill penalties come in; subtracting a penalty from the PC's skill level to reflect exceptional difficulty. The penalty can potentially make the chance of success fall below zero, so the novice might have no chance at all, and at a minimum the expert would need to be skilled enough to have even a chance at success. (It's a kind of threshold itself, but one without assured success.)
