I’m going to throw my sample-of-one 2c into the ring here:
I believe there is a most efficient method at least as far as getting to intermediate is concerned. It’s this:
If you don’t have five years of free time or a year in jail you need to optimize.
98% of all spoken language consists of the top 5,000 most frequent words.
It therefore stands to reason that deliberately memorizing those words (somehow) instead of waiting for them to appear should be more efficient.
Here’s why… The human brain (and the rest of the human organism) has evolved to not use more effort than strictly necessary in order to do anything.
Therefore we have evolved to accumulate the minimum necessary number of words in the most likely scenario that a human being would have (small village worth of input). Lets say it’s the average 10 year old villager’s level we would consider to be advanced fluent. We can speculate how many hours of input that is (X total hours to get 5,000 words memorized).
If brute memorization gets you those 5,000 words memorized in less than X total hours of effort then it is de facto more efficient. If it does not, then it isn’t. Just math.
Likewise, the same can be said of output. The average 10 year old villager will have Y hours of natural outputting in a stress free non-drill environment. If your deliberate practice method will get you the equivalent output in less than Y hours then it’s more efficient.
In both cases I believe you can. The question is “by how much”?
That’s a more tricky answer and the devil is in the details. The first point is deciding what is the baseline. We’re all over the map here.
For that reason I think it’s important to define what is your goal specifically.
I can say with 100% confidence that I can get to listening comprehension of classroom style speech in any language with just input and anki memorization in six months.
I will not be able to get to classroom language level of output with only that. Nor will I get to my eventual goal of being able to understand netflix shows without subtitles. Something else is required for the two additional goals and I haven’t figured out what it is yet.
We may speculate but I think deliberate practice is likely part of it. Steve Kaufmann for example tends to start talking to natives when he “feels ready” to improve his output. Clearly Steve does not believe his input will magically enable him to speak perfectly or else he wouldn’t do his output piece
Michilini said (probably correctly) that native Chinese won’t understand you unless you drill tones. His English university buddy drilled tones (among other things) and is “wow he’s so amazing” levels of speaking.
In my own case I believe cases in Russian cannot be acquired for active output without drilling.
TLDR
Anyhow end result yes I believe some combo of deliberate practice and input is absolutely necessary to get past intermediate.