> It's very well known that Chinese grammar is super close to English for whatever reasons.
They are both felt to have gone through a lot of simplification. It isn't well known that they have similar grammars, for the fairly straightforward reason that they don't have similar grammars.
As an English speaker I find it frustrating that languages like German and French have so many irregular verbs and that you also need to keep track of grammatical gender which seems pretty arbitrary.
In Chinese though you find structures which are pretty regular such as "measure words" where you might write
yi zhang zhi
which means
one (piece) of paper
where the word "zhang" is used because paper is thin, but you might use "ke" for something round like a pebble or "tiao" for something long and flexible like a snake. This and a lot of of what I read in the grammar book comes across as rational to me.
Note that Latin is generally considered to have about four irregular verbs, possibly a few more than that depending on how you're counting.
A verb in Ancient Greek has six principal parts, which means that to correctly inflect it you need to memorize six more-or-less independent forms.† (They're often "less" independent, but sometimes they'll surprise you!)
By contrast, an English verb, except for the single verb be, has a maximum of five forms. (Not five principal parts - five fully-inflected forms!) So by the Greek standard, English has just the one irregular verb. That's not a correct application of the concept, but it is worth observing.
> I don't think French has examples as crazy as go -> went. I mean, there aren't even letters in common!
This is a suppletive verb. (That is, a verb in which some forms descend from one ancestral verb and other forms descend from a different ancestral verb.‡) Went was originally the past tense of the still-existent verb wend, in the same way that bent is still today the past tense of bend; wend has had to shift over to wended.
Not only does French have suppletive verbs, it has the same suppletive verb, aller [to go]:
1sg pres. je vais [< Lat. vadere]
1sg impf. j'allais [< Lat. alare]
1sg fut. j'irai [< Lat. ire]
The Latin verb is ire; it is minorly irregular but not suppletive in Latin. Suppletion is present in Latin anyway; the best-known example would be fero, whose third principle part tuli is taken from tollo. In turn, tollo uses sustuli [= sub- + tuli] as its third principal part, and then sustuli is left ambiguous between being the perfect form of tollo or of suffero [= sub- + fero].
Circling back around, we can note that while fero is one of the rare Latin verbs that comes with a warning that its conjugation is irregular, that's not because its perfect forms are taken from an unrelated verb. By itself, that would barely be worth remarking on.
† And this is a convenience for modern students. Actual speakers of the language would have thought about their verbs a bit differently - in a number of common cases, one of the principal parts is a form that doesn't otherwise exist in the language, which native speakers would never have considered.
‡ Suppletion as a linguistic phenomenon is not restricted to verbs; compare person -> people.
They are both felt to have gone through a lot of simplification. It isn't well known that they have similar grammars, for the fairly straightforward reason that they don't have similar grammars.