In my post about Active Phonology, I said that phonological features (which I feel should be privative as opposed to binary) aren't properties of the sounds; they're instructions for making the sounds. And these instructions (or gestures, or "actions") are all you need in the phonology. The sounds just give you a hint as to which gestures are being performed in the vocal tract. (This explains why in an experiment, when the audio says /k/ but the lips in the video say /p/, participants will believe their eyes and not their ears. It also jives better with signed languages, which don't have any sounds at all.) Since the features/actions are all you need, I took care to name them accordingly, with a clear relationship to the surface form that comes out (rendering features like [hold] instead of [long], verbs not adjectives).
Extending this to morphology and syntax, morphosyntactic features don't trigger a certain surface form and/or semantic interpretation; they're linguistic signs just like everything else. And as such, they're entitled to both a form and a meaning (though either or both may be a little hard to spot). Let's take a really obvious phenomenon in English and see what it looks like with the sort of analysis I'm talking about: plural nouns. (I'll just use a fairly standard American pronunciation here.)
- cats = /kat/ + [plural]:[s]
- dogs = /dAg/ + [plural]:[z]
- boxes = /bAks/ + [plural]:[@z]
- children = /tSAy@ld/ + [plural]:?
- people = /pUrs@n/ + [plural]:?
- ploobs = /pluwb/ + [plural]:[z]
Pretty standard phonological analysis of the situation will tell you that [z] seems to be the underlying form of this plural morpheme. It has the least restricted (hardest to describe) environment of the three productive plural affixes. So you might say you have a morpheme with a phonological form /z/ and a meaning [plural] that can get attached to nouns without this meaning (i.e. singular nouns).
So why don't we say "childrens" or "peoples"? (Well, the first one may be sociolectical, and the second is perfectly valid when referring to large groups of people, but you know what I mean.) We don't need to because "children" and "people" already contain [plural] as part of their meaning. Why don't we say "childs" or "persons"? Well, why should we go to the trouble of adding on the [plural] morpheme to build new words from scratch when we already have what we're looking for pre-built in our repertoire? I'd say that irregular forms are allowed to exist precisely because the language system searches the (enormous) lexicon first and only resorts to applying a generalized rule when it's absolutely necessary. The brain is fast at finding things (given proper context), but not so fast at processing.
If this is the case, why would the general rule be applied to some really common words like "cat" and "dog", making them more work than irregular forms? My answer is, it's not! These plural forms are certainly common enough to be listed in the lexicon just like "children" and "people". Of course, if they were being built on-the-fly, they'd look exactly the same. A word like "ploob", on the other hand, probably needs the rule generalized from words like "dog" to add the plural /z/ morpheme.
Imagine this sort of thing applying all over the place in the grammar. Not just to form words, but to form sentences and dialogues. It means we'd need lots of space in our brains (which we have) and that language should be surprisingly easy to process (which it is).