Many servers follow a specific system for clearing tables, so customers stacking the plates themselves at the table might well mess with that system and create more work for them.

When a server takes plates back to the kitchen, they may need to remove scraps and load the dishwasher, which would require them to unstack the whole pile and make it messier.

Stacking plates can send a signal that your server isn't performing their job correctly. Some customers may overstep by stacking plates as soon as people have finished.

This is despite the standard for servers to wait until all diners are finished before beginning to clear the table. It's best to leave this task to the professionals.