I've encountered the effects of ignoring Russian grammar and the results are more often than not awful. A purely lexical approach without grammar or vocabulary study doesn't work in all situations for all people.
The lexical approach is about studying "grammaticalized lexis" i.e. it does away with the dichotomy of grammar and vocabulary as separate study subjects.
Anyone actively studying lexical chunks cannot possibly be ignoring vocabulary. While grammar plays second fiddle, it is hardly ignored. Paying attention to lexical chunks could prove especially useful while studying a highly inflected language like Russian. Nobody's forcing students, teachers or self-learners to adopt this approach. What's more, the lexical approach is apparently largely ignored:
"A quick glance at any commercially available EFL textbook reveals that a traditional grammar syllabus, the main object of Lewis's attack, is still alive and kicking, albeit more cleverly disguised."
https://www.google.com/amp/s/amp.thegua ... revolution
As Nick Ellis (2011, p. 656) puts it:
"Adult language knowledge consists of a continuum of linguistic constructions of different levels of complexity and abstraction. Constructions can comprise concrete and particular items (as in words and idioms), more abstract classes of items (as in word classes and abstract constructions), or complex combinations of concrete and abstract pieces of language (as mixed constructions). Consequently, no rigid separation is postulated to exist between lexis and grammar."
https://scottthornbury.wordpress.com/20 ... struction/