grammatical number - Why do we use plural for indefinite objects?

Building off another question I answered here, I couldn't justify why exactly we say:

I like to ride bicycles.

Instead of:

I like to ride a bicycle.

(This could be anything: "climb mountains", "fly helicopters", etc.)

Both of these forms should refer to some generic, indeterminate bicycle object. But we can't ride more than one at a time, nor do we mean to say that we like to ride them one after the other, so how does the plural form work here?

Even though the second example looks like a valid construction, it just doesn't sound right. I suspect it's because the indefinite article "a" adds something when used in this sense, instead of just meaning to say "a bicycle" in the generic sense, it implies:

I like to ride a (particular kind of bicycle).

However, "I like to ride my bicycle" works. Is it because "my" makes it less generic, or just because it means "the one that is mine"? So why does the indeterminate "a" not work in the same construction?

(The only sense where "a" seems to fit is when using the conditional: I would like to ride a bicycle. But again, this has a slightly different meaning than I would like to ride bicycles, in the general sense.)

How should I understand what's happening in these constructions?

Answer

The reason I like to ride a bicycle doesn't work is because the singular indefinite article implies there's just one particular bicycle you like riding.

When you say I like to ride bicycles there's an implied plural indefinite article there, but we discarded that word centuries ago. We're so used to not using it we don't even notice it's not there.

Even though the article is missing, we understand as if it were there; we don't suppose OP likes riding more than one bicycle at a time - he likes riding [some, most, many, all, any] bicycles.

I think the success of this usage encourages us to discard the singular definite article in various related contexts. So I like to play the piano, is increasingly giving way to I like to play piano (even more noticeably with the more modern I like to play guitar).