Man-men.
Woman-women
Go-went-gone
Do-did-done

Yes, I know. We don't talk about oxen that much anymore, but at the time when English was becoming standardized, most people were rural, and oxen were commonly used as beasts of burden. And there were undoubtedly more mice running around then than there are now.

Then again, some very common words developed regular plurals, such as "shoe" (which used to be "shoen&quot and "book" (which would be "beech" if the old plural had been kept and developed normally).

The main claims extant in the literature was that very high frequency words and very low frequency words would be immune to leveling, to regularization.

Very high frequency words are learned as isolated words and never fully integrated into a paradigm. Each form is learned separately and there's no overriding need to put them into some sort of pattern. Or at least not into the main pattern.

Very low frequency words can have quirky phonology and morphology because their quirkiness marks them (not in any Prague School sense) as low frequency.

The rule isn't so much a rule as a statistical tendency for innovation of irregularity and innovation of regularity in different contexts. The UR dissertation, IIRC, employed a network model of associations between lexemes and paradigms, coupled with some sort of stylistic/frequency-based metric. Not a quick read, if you look at the details.

When the words became "irregular" also matters and the extent to which they seem to fit into some sub-phonology, into some less common but still regular pattern, also matters. As long as "teeth" looked like it was "tooth" + ending that triggered the regular fronting of /o/ it wasn't irregular. Words like "ride" were regular but were taken to be in the same category with "irregular" verbs with a vowel change more or less regular for verbs in that category.

Last I heard "children" was a linguistic basket case without a good solution, or at least without a solution that was really plausible and provable. The /r/ or the /en/ doesn't belong there. IIRC, the -en was original in the dialects that produced the core of English. My standard guess is "hypercorrection" needs to be invoked--people heard forms ending with /r/ (parallel to German Kinder) and forms ending with /en/ and merged them in a non-regular, unpredictable way. Better to have both endings than leave off the right one.

while the "-s" "-es" is French.

So, all other plurals are irregular, like German (as you mention) and lots of Latin, as in "media", "paraphernalia", "alumni", or Italian, as in "spaghetti".

As Lydia says, it's the really old, basic words that tend to be weird (they've had more time to get mucked up), and as gd says they often come in via German. Two of your examples have dropped from PIE (relatively) unchanged: '*uks-en' and '*muHs-'.

'*ped-' has been on a bit of a journey to become 'foot' and '*dont-'/'*dent-' to become 'tooth' (but seem to have survived into Latin OK) and PIE 'g^u̯elbh-' -> PGm '*kiltham' -> OE 'cild' -> 'child' is sort of visible if you squint.

What's funky about 'child' is that the OE 'cild' was both the singular and the plural (a bit like sheep), but it was then re-pluralised in the 12th century: The resulting 'children' looks more like the PGm '*kiltham'. Prediction for the year 10,000: Children we be called 'gelfs' as we regress to PIE.

As an aside, I-mutation is common in these old words from their passage through German.

cath, cathod cat. cats
ci, cwn dog, dogs
plentyn, plant child, children
bachgen, bechgyn boy, boys
merch, merched girl, girls

and when counting something it's common to use the singular unless using the conjuction "o" (of):

three dogs
tri chi ("three" causes aspirate mutation)
or
tri o gwn ("of" causes soft mutation)

But it's the past tense of "wend".

send -> sent
bend -> bent
wend -> went

Somewhere between 1200 and 1500 "goed" was replaced by "went", first by deliberate use of "wend" in place of "go", and later when the connection between "wend" and "went" was pretty much forgotten and "went" was just thought of as the past tense of "go". (At which time a new past tense for "wend" was invented: "wended".)

The process is called "suppletion", and is how four entirely different verbs with similar meanings gave rise to four different forms of what is now thought of as the same verb in "is, am, are, was".

It's also the way two originally unrelated nouns, "person/persons" and "people/peoples" got muddled together so that the singular of "people" started being used in place of the plural of "person". Why does it happen? Mostly through ignorance, the single greatest force in the evolution of languages. Back in the 1200's not only was there no Internet, there were no grammar police to tell the ignorant fools they were using English improperly. Their stupid mistakes have been cast in stone and are now our rules of proper English. Their errors have become our irregular verbs.

The phenomenon occurs in all languages. Look for it wherever one form of a word is clearly not from the same root as another. Mother->motherly is NOT suppletive. Cow->bovine is.

are the principal parts of one Classical Latin verb, but they appear to be derived from what were once three different verbs.