Is it grammatically correct to use could in this wish-clause?

To me, "could own" means something different from "owned": (a) means that I don't own a motorbike, and I wish things were otherwise. (b), on the other hand, implies not just (a), but also that there's something blocking me from owning a motorbike, such as a law or city ordinance.

However, (a) I wish I owned a motorbike. (c) I wish I could have a motorbike. sound nearly-synonymous to me.

The "I wish" structure usually demands that the following verb be/is put in the conditional mode in many languages, including in English. In English a past tense modal verb like "could" is used. Here is the explanation.

Past tense modals would and could are used about wishes for the future:

• I don't like my work. I wish I could get a better job.
• That's a dreadful noise. I wish it would stop.
• I always have to get home early. If only my parents would let me stay out later.

Past simple and continuous are used to talk about wishes for the present.

• I don't like this place. I wish I lived somewhere more interesting.

So, let's compare using the first example. I could say:

• I don't like my work. I wish I had/got a better job.

VERSUS

• I don't like my work. I wish I could get a better job.

In the first example, the person does not give the impression that it could happen, that it can be possible that he or she could get a better job.

Still, the question has this: "You don't own a motorbike and you need one. " This would tilt the next sentence to use the "could" because there is a desire or a need to need one.

https://learnenglish.britishcouncil.org/english-grammar-reference/wishes-and-hypotheses