Why is "afford" always accompanied with "can"?
Solution 1:
The meaning of afford we are considering here is that which the OED gives as its fifth definition: ‘To manage to give; to spare (time, room, money, etc.)’.
That, by its nature, is not something we do or don’t do. It’s something we are able or unable to do. When we try to substitute spare for afford, we encounter the same problem. We don’t say of something expensive *‘I don’t spare money for it’ any more than we say *’I don’t afford it’.
Solution 2:
The premise of the topic is false. "Afford" is not always accompanied by "can." In the sense of this meaning, "to make available; provide" (Am. Her. Dict., 4e: def. 4), its use in this sentence is straightforward: "A walk in the woods on a beautiful autumn afternoon affords me great pleasure."
Granted, this does not resolve the question of why "afford" is accompanied by "can" in the sense of capability of giving up something of value, whether monetary or otherwise.
Solution 3:
The question has been answered, but because the additional discussion wandered a bit, a brief summary seemed warranted.
Etymologically (OE geforthian, the ancestor of, among other things, ModE "further") and historically, "afford" means "advance, make available or possible."
In the senses indicating an ability or capacity to take advantage of an opportunity afforded by some development, the word requires a modal auxiliary, whether "can," "may," or some of the other suggestions made.
These are the meanings in the OED's section III, which specifies the need for an auxiliary. In Middle English, the auxiliary is "may" (MED aforthen (b)). Modern American dictionaries regrettably confuse matters by including the meaning of the auxiliary in the definition. Used without an auxiliary, "afford"'s meanings all derive from the sense of "further."
Solution 4:
The essential meaning of "to afford" is to provide or offer something.
Buying this car would afford me great pleasure.
The meaning is similar when used with can, except that the thing being provided is usually implicitly understood to be the cost or price of the verb's object. In your example,
I cannot afford this car.
means
I cannot provide the money needed to buy this car.
Solution 5:
From the OQ:
To me, "I cannot afford this car" means "I am not able to have enough money to be able to buy this car".
The reason can is used with afford is because people use the word afford as a substitute for the word provision or provide for or allocate/furnish funds for/to.
The common usage, per Wiktionary:
To give, grant, or confer, with a remoter reference to its being the natural result; to provide; to furnish.
Per the original quoted definition, afford is defined as [already] having the money to be able to pay for something. But people don't use that definition when they say "afford". That is to say, English usage of afford in this context is about furnishing of funds rather than having the funds.
"Can you afford to pay for that new widget?" Means: Are you able to furnish the funds to pay for the cost of the widget?
Yes, to afford means in one definition to have the money to be able to pay for something, but it's not just about having the money (to an English speaker). It's also whether the money can be furnished to pay for it.
Per questions:
Why not I do afford this car?
Because do [verb] is almost always used with thinking and feeling verbs, especially for emphasis:
I do like you.
I do like to see this movie.
I do think you're going to like this.
You're not going to do afford this car. You either can afford/furnish funds for the car or you pay for the car.
Q: Do you afford this car?
A: (Do I afford this car [what]?)
vs
Q: Can you afford this car?
A: Yes
I do afford this car is incorrect simply because the statement isn't finished. That is to say, the sentence needs an explicit object that is being afforded to the car.
Rewording for I don't afford this car: no difference in the summary statement. The sentence needs an explicit object that is [not] being afforded to the car.
You don't afford the thing to do or to buy. You afford the means to do or buy.