Do native speakers generally think of うまくいく as a verb phrase or a full-fledged verb? I’ve noticed that うまくいく is paired with adverbially inflected i-adjectives instead of the continuative form–i.e., 多くうまくいく not 多くてうまくいく. If うまく was parsed as the adverb form of うまい, I would expect the latter, not the former.
Here’s a contextual example:
あなたのことだから間違いなくうまくいくと思うよ
A quick Google search shows 1400+ examples of ～くうまくいく and only three of ～くてうまくいく.
Note: this is my probably flawed and possibly wrong understanding, not objective fact
It’s a verb phrase (you can think of it as a set expression, but I don’t think that’s what’s at play here).
With regards to your examples, the reason for not using the て form is those adverbs modify うまく, not 行く. For example with 多くうまく行く, things do not “go frequently and go well” as 多くてうまく行く would imply, they go well often. Same with 間違いなくうまく行く - what’s unmistakable isn’t that things go, it’s that they go well.
Consider a different verb phrase with a different adverbs:
よくて速く走る - I run often, and I run fast
よく速く走る - I often run fast
Both are correct, but they mean different things, and in the case of うまく行く it’s just not often the case that a second adverb would also modify 行く as opposed to うまく, I suppose.
One of the cases I find is, for instance ちょろくてうまく行く, which is one of those few cases where it does make sense for both to act on いく- it goes both well and easily.
You know, for some reason I thought it was not grammatical to have multiple adverbially inflected 形容詞 like this. Now that you’ve pointed out it is, this makes complete sense. Thanks!