Certainly an interesting thought. The Russians, Prussians and Austrians used the solid square. Much of this came from the the experience against the Turks where infantry had to advance across open plains.
Advantages of Open Squares
1. Open squares were larger and permitted more muskets on each side.
2. Less of an artillery target
3. Officers horses could be easily contained in the centre.
4. Easier to give refuge for gunners from supporting artillery.
5. A brigade would take up more ground in open square than closed square.
Advantages of Closed Square
1. Faster to form from column of divisions
2. More maneuvreable than open column.
3. Less training required to form. etc....