What is considered incorrect for a cladogram's time axis?
In your first example, each species becomes "frozen in time" once it evolves implying there is no further change. A slightly more complex cladogram will help.


Imagine the species A ancestor, after branching off the remote ancestor, serves as the ancestor to species E. You need to draw that line in some direction other than along A. Most popularily, that line would extend upward to the right. With the temporal axis as you first show, how did species E even evolve since A is frozen in time? Furthermore, the advantage of a vertical time axis allows us to see that species E appeared after species B and a bit before species C (horizontal dashed line).