I loved the Doors.  Personally I'll take those over sidequests for Towa, school house, sidequests on field study, to finally the peak of the story part of the chapter.  Not just CS1, but I guess sidequests in general for the series.  A big part is because I could put off the doors if I really wanted to.  Sidequests I couldn't, so I had to do those right away regardless of how absorbed I was into the current story if I wanted to do everything.
It felt like it trimmed a lot of the fat for Trails game for me.  Also worked out on how fast the game threw better quartz and characters to you, imo.  Plus some of the doors (especially later on) allowed them to write interesting little snippets without figuring out how to shoehorn them into the main plot.
The 3rd's probably my third favorite of Trails though.  I didn't find it too out of place compared to the rest of the series, but I can see it has enough to throw people off and not enjoy it as much.