> English has ... subjunctive / conjunctive / conditional («went» in «as if they went»)

That isn't the English subjunctive.

You're correct that this construction expresses the same thing that another language might express by marking a non-indicative mood on the verb, but it would not conventionally be said to use a non-indicative mood. That went is a normal past-tense indicative verb and the modality is expressed by the whole structure of the clause, not just by the inflection of the verb.

In linguistics there's a whole set of parallel vocabulary where one set is for grammatical forms and the mirror set is for the semantics usually expressed by those forms. So you have grammatical "tense" and semantic "time" or grammatical "mood" and semantic "modality". You got the modality right, but not the mood.

Compare the conventional analysis that he will be there tomorrow expresses future time, but is not in future tense because there is no English future tense.

> That isn't the English subjunctive.

No, it is not a proper English subjunctive (a correct example would have been «as if they were» – past subjunctive) or «[we suggested] that they go».

I deliberately lumped subjunctive, conjunctive, and conditional together for brevity. Part of the problem is that many English speakers do not differentiate between subjunctive and conjunctive (conditional) and incorrectly label the latter as subjunctive, but that happens because English does not have a conjunctive (conditional) mood.

English subjunctive is translated into other Indo-European languages either as the conjunctive or indicative mood, as there is no 1:1 mapping in existence.