There shouldn't even be formal rules. The meaning of linguistic constructs are determined by how the appropriateness of phrasing is captured by usage in context. Whether "old little lady" or "little old lady" is correct is largely a matter of what you are more comfortable with, which is a matter of how people around you spoke when you learned the language.

Formalizing it would be about as silly as formalizing which music sounds good.

Sorry, I think that's complete bullshit. And there is indeed a great deal of theory that formalizes what makes music sound good; most of it is maintaining patterns of whole-number ratios to derive scalar and rhythmic intervals, and there are certain algorithms and formal rule systems that reliably produce pleasing results within particular genres. Even music that deliberately breaks these rules (like 'noise music' involving extreme distortions or recordings of 'unmusical' sounds) can be thought as a meta-development of those rules; the equipment or source material employed to make such 'unmusical' sounds acts as constraints, and lead to emergent structures of their own.

I would disagree with you, but the problem here is that we are communicating different concepts using the same words.

Well, I don't wish to get in a fight and I'm sorry if my blunt response came across as a personal attack. I'll try to keep a more open mind and work harder at understanding your perspective rather than just restating my own.

I think you're confusing linguists with usage mavens. This type of research isn't prescriptive -- it's descriptive. The "rules" are attempts to describe how people actually use English, in a variety of contexts. If common usage changes, the rules would change.

Saying the rules shouldn't exist is like saying Newton's laws shouldn't exist -- they are just patterns that someone has noticed.

While there seem to be exceptions to most rules proposed (because natural usage is complex), the rules are still fairly accurate for most cases.

The primary use of these rules, in my experience, is to prevent the common usage from changing. You certainly don't do a good job teaching language by asking people to memorize formal rules. You also aren't going to make a computer understand natural language by writing down formal rules.

So why do it? To make observations? Observations don't need formalization; just provide good statistics.

Do you mean that the phenomenon of language should not be scrutinized to discover rules, and thus that there ought not exist the field of linguistics?

(If that isn't what you mean, then what do you mean? That linguists should carry on, but not look for patterns and rules? Then what, instead?)

Also, what is a "linguistic construct" if we don't have formal rules? Whatever it is, wouldn't it be less ironic to call it a "speaking thingy"?

No, what I mean is that the rules are only at best heuristics for mimicking another style of writing. They're not correct or incorrect, except so far as they are poor representations of some specific culture.

To say there are formal rules of language is a bit like saying there's only one culture that is fit to judge the acceptability of your words.

Yeah, any time I see something like this I think, it would only take a couple of widely read books or widely watched TV shows breaking these "rules" to change what "sounds right" to a lot of people. Having said that, studying the evolution of these sorts of idioms over time seems fascinating to me.