Any grammar rule is necessarily a gross oversimplification of what's going on in the mind of a speaker of the language. How can we expect it to work? It doesn't. Learners that only know rules and are forced to use them develop their own "interlanguage", far from the actual target
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Learners develop their interlanguages through natural acquisition approaches too. The existence of interlanguages is not argument against teaching grammar rules. There may be others though!
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I disagree with the premise that a learner has to go through an intermediate step of a mixture of the L1 and the L2 before reaching proficiency in the L2. The L2 can be built separately, but of course if you make students produce before it's built a lot of L1 comes out.
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On your second point, that isn’t always true. With well scaffolded TL lessons you can use pushed output to great effect without students resorting to English. Indeed, repetition, reading aloud, QA drills etc all build phonological memory and therefore improve acquisition.
It may be possible to bypass L1 but certainly not optimal. L1 is a rich asset for L2 acquisition, e.g. French, Spanish, & German have a lot of syntactic & lexical similarities with English.
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If you can, check out "Acquiring Information: The Borrowing and Reorganising Principle and the Randomness as Genesis Principle." Sweller, J., Ayres, P. L., & Kalyuga, S. (2011). Cognitive Load Theory (pp. 27–38).