I am unsure how well I am contributing towards this discussion, as I have minimal experience/knowledge in 20th century analysis. However, I can offer some points on how such analysis can be applied to music produced by common practice composers of the 18th century.
The vast majority of composers of this period are thought to have been trained in a manner closely aligned with the pedagogy of the Italian school, in particular the Neapolitan School. To provide some context, 'Conservatories', as they were called, were once established in Naples during the 16th century to address the high orphan rate, and was a joint initiative between the Spanish State and the Roman Catholic Church. These schools helped to 'converse' the young and vulnerable and, in conjunction with meeting their basic needs, provided some form of education . Over time, many such schools became specialized and renowned centers of learning (for instance music conservatories) and to a considerable extent during the 17th and 18th centuries, served to provide the church and aristocracy (the two principle employers of musicians at the time) with professional and highly skilled musicians & composers. Of course, many of the widely known composers of that era were neither orphans nor educated at such places; however, often wealthier students who could be afforded private instruction would be apprenticed under a master, well versed in the prevailing practice.
There is much renewed interest in these music conservatoires, for the reason that it was their transmission of knowledge, spanning centuries, which underpinned the greatest works of that era. The study, however, such such institutions, is rather hampered by the fact that most knowledge was aurally transmitted. Whilst there are surviving documents which provide instruction to students (such as those by Fenaroli and Giovanni Martini) the vast majority of publications are merely exercises. Those exercises are what we call 'Partimenti'. The importance of Partimenti cannot be understated. They contained conventional patterns which were standard of common practice, and the success of the student largely depended on their means to recognize those patterns (for instance, ascending 5-6 suspensions) and recalling their associated realization between the other voices. At beginner to intermediate level, typically only either the bass or treble clef would be populated. The relationship between improvisation and partimenti, therefore cannot be understated.
It is difficult to do this subject justice with only a couple of paragraph's, however I have hoped to illustrate why it is probably a bad approach to assess music from this period with modern theoretical principles. Students of the common practice period largely learned by rote, at least in the beginning, which of course was very practice orientated and less theoretical. When I analyze music from this period, I typically listen to patterns; And it is patterns you learn to hear and recognize. Have you ever wondered how Mozart managed to compose grand works within a matter of days? Well, he was a master at improvisation and his extensive mental library of ideas were without question deeply rooted in the preceding chapters of music history. And he was not alone in his means to compose quickly; This was a skill expected of the professional composer and I suppose further illustrates the importance of understanding how to apply and manipulate 'patterns, so to speak. Of course, as we move more towards the 19th century and beyond, those patterns are still applied however without the intensity of some of the earlier 'galant' composers.
My post below talks about these patterns in a little more detail
https://www.youngcomposers.com/t38646/largo-for-winds/