ZZ blockbuilding is more "restricted" than petrus or roux blockbuilding. This is because edges have fixed orientations, and only <RUL> moves are permitted. In this sense, ZZ blockbuilding is easier than the others in that there are far less "block cases" to deal with. [Some will argue that this makes ZZ less efficient. That is false theoretically and experimentally.] This also makes it easier to determine which cases are easier than others. In roux or petrus, the solver needs full-cube awareness to take advantage of the easy cases. In ZZ, because you can always see all pieces that you need, it quickly becomes a sinch to pick out ~4-5 move squares and ~11-12 move blocks at full speed.
The alternative that you propose is basically solving Eoline and then place the DR and DL crosspieces (called EO-cross). This is a viable option. It's just less efficient. I'm sure a few ZZers place a cross piece whenever they get a chance, but in the long run ZZ capitalizes on its "restricted" blockbuilding.
Also, there a bunch of people that switched to ZZ in hopes of avoiding 60 OLL algorithms (myself included). However, the truth is that you will eventually learn 40+ coll algorithms, a bunch of winter variation, and perhaps some CPLS, so that in the end, you won't really have "saved" any algorithms.