While it is true that students tend to start off with books giving legal conclusions divorced of their evidence, the second or third book in most study programs includes evidence and alternative opinions within the school and across other schools. Some books include it all, some books focus on particular aspects. But in the end, students did read a series of madhhab specific books that covered issues, alternative opinions within the school, alternative opinions in other schools, and the evidence for each.
In addition to madhhab specific books, students would read books focusing on the legal interpretation of verses of the Quran and Prophetic hadiths. These books would give various opinions and then argue the merits of each, finally concluding which was best. Obviously: “which was best” depended upon the author’s school of usul.
While not everyone who started a study program finished it, people did finish it, so people did have knowledge of alternative opinions within their school and across the schools, just as they had the evidence and reasoning being those various opinions.
Offering public lessons with evidence is nothing rare, even today. This is patently obvious for anyone who has attended a Friday Prayer or sat in on public lessons at the mosque or local Shari’ah institute.
As for scholars offering (and following) opinions that are not the strongest according to their school: it doesn’t take much reading to find examples of “X opinion is the official opinion within the school, but in practice we do Y” or “we give fatwa according to Y”. Some schools, notably the Hanbalis, considered it recommended for a judge or mufti to send petitioners to scholars who might have a more suitable opinion – even if the scholar doing the sending considered the opinion weaker than his own. And in this, the Hanbalis are not unique.