In a proper multi wire circuit (each hot being from a different side/leg of the panel) the current load on the neutral is the difference between the two hots. If you were to use hot from the same 120V leg the current load is added, depending on wire size and devices on the circuit, an improper multi-branch circuit could overload the neutral.

And yes as you said, dropping the neutral on a properly wired multi-branch will give you some other problems, but not necessarily 240V.

[Link: ecmweb.com]

There are risks in either situation.