This is a valid point. I'm teaching a compilation class to undergrad computer science student, so we actually first learn each "horizontal" step separately and work on them during lab session, and then for their project I strongly recommend that they take the "vertical" approach, because it is systematically what gives the best results.

In a sense, even if my student's project is their first compiler, they already saw and did exercise on each compiling step individually, a bit like you said.