Hey Andy,
to buy a machine that really will wobble if you put a coin under one of its feet, I think you would have to spend the price of a car for it. There exist such machines, they are made of extremely thick rolled and/or casted steel and their frame is usually annealed for stress relief with temperatures of 550 – 650 °C in gigantic annealing furnaces like shown here and here.
If such a machine would really wobble, there would be acceleration and deceleration forces acting on all parts. Depending on how much it tilts and how large the masses of the moving parts are (e.g. X gantry with Z slider and milling motor), I would not exclude that it is possible that you impact the work process, e.g. make the machine loose steps on a stepper motor.
But I don’t think someone will first buy such an expensive machine and then let it wobble 
But who knows.
PS: The cheapest machine I know which is made as described above (welded out of 10 mm thick rolled steel profiles and annealed for stress relief) is this one for Journeyman size. But I don’t know if it is already stiff enough that it would wobble if you put a coin under one of its feet. Note the price is without steppers, controller, spindle and table.