It's not that grounding through the 'low' outputs "won't work". It's about how well it will work, and what problem does it solve. What are the trade offs?
Your logic levels are degraded. The 3.3V "high" (which was really less than 3.3V) is robbed of a diode drop or a Vbe, or both.
If you do have two outputs such as PA0, PA1 high, then their 8mA+8mA will both want to flow somewhere else such as PA3 (which is already carrying 8mA from PA2).
If somebody walks across a carpet on a dry day and generates a 1kV spark (well below what you would notice) on the robot, it will flow through PA0..PA7 towards the earth on the microcontroller chassis and the wall wart. Microcontroller inputs are likely to get fried.
Incoming electromagnetic noise such as from nearby (1km) radio and television broadcasters (or very nearby cell phones) may cause unexplained upsets. Similarly, an Earth accompanying signals can reduce the likelihood of causing interference to others.
Advantage: If all of the PA0..PA7 lines are driven high (or floating), the motors will shut off. This protection is defeated if any line is driven low, in which case the sole low PA signal is overloaded.
[edit] As usual, I'm the slower typist. [/edit\]