"talk over the phone" or "talk over phone"

We just talked over the phone.

Is what I've always used. I believe by "phone" we mean the phone lines, or phone system, rather than any physical phone.

You need either an article or some other indication of number -- like "one" or "any" -- pretty much any time you use a singular noun that is not a proper noun.

So if you want to make clear that it's not a "specific phone", you could use "a" instead of "the", but you need something. And in the case of telephones, we pretty much always say "the phone" even if it isn't some specific phone.

You could argue that logically it should be "we talked over the phones" -- plural -- as you do indeed need two to have a conversation. But for whatever reason, nobody says that. The convention is to say "we talked on the phone".

I suppose, especially with articles and count/ noncount nouns, it isn't really a good idea to stick to the physical realities like what you're thinking.

Take for example: "on foot."

Following your guideline of specificity, I should probably say "go there on my foot."

And following your logic of paired necessities, I should probably say: "go there on my feet."

But we all know the expression is "on foot" and not "by foot," "by walk" or anything else.

In any case, the same flawed logic is at work when non-native speakers experiment with idiomatic expressions by trying to make them conform to other realities (whether based on their native languages or not).