It's an interesting coincidence, but I think there is a reason that the te-form in Japanese is much more fruitful than "and" in English in producing these constructs. Japanese verbs have too conjunctive forms: te-form and ren'youkei[1] (continuative form). Ren'youkei、 is more formal and has a different but overlapping range of conditions in which it can be used. The "te-form" itself was originally[2] just the ren'youkei conjugation of a special auxiliary verb "tsu", that is used to mark a completed action.

Neither of these forms is nearly as flexible as the conjunction "and" in English. For one, they can only connect verbs and one class of adjectives, but another important point is that the actions described by the verbs need to occur sequentially in time, with the action marked by '-te' occuring earlier. You cannot use either of these forms to say something like "The dog kept jumping and wagging its tail" or "It's important to both eat and drink".

If we compare this to how linguists define "pseudocoordination" in English and other Germanic languages, then every instance of the te-form or ren'youkei in Japanese is pseudocoordination and not real coordination: you cannot reorder the verbs freely, you cannot add "both", and you can use an interrogative pronoun. Since these limitations apply to every use of the te-form and ren'youkei, not just the "special case" ones, it makes these form more amenable for building special construct. Add the fact that Japanese does not have an infinitive form, and you end up with either of these forms as the most natural way to attach auxiliary verbs in Japanese.

Now you end up with a plethora of constructions (demonstrated with the verb 作る tsukuru "to make"):

  作ってみる   tsukutte miru    (make and see) try to make
  作ってみせる  tsukutte miseru  (make and show) prove that [I] can make it
  作っていく   tsukutte iku     (make and go) gradually make (or make more and more)
  作ってしまう  tsukutte shimau  (make and complete) finish making or "oh shit he really ended up making that" (the MORE common meaning in this case)
  作ってください tsukutte kudasai (make and give (imperative)) Please make
 
 

[2] https://old.reddit.com/r/LearnJapanese/comments/v08pbp/brief...