If Mendelev hadn't put the periodic table in its current order, would it still have been made popular?
The periodic table is very different to things like the QWERTY keyboard layout which is essentially arbitrary.

The structure is determined by the fundamental chemical properties of the elements. When the table was first developed Mendeleev was wise enough to arrange the table with both gaps and with some elements in chemical property order rather than the order indicated by know physical properties such as atomic mass (which usually gives the same order as chemical properties but gets it wrong a small number of times). 

These properties are fundamental to the elements and not a matter where human choice can have any impact at all. Sure, there are alternative ways to get the graphic design right, but none of these work if the violate the original principles of grouping similar elements together. Therefore, no alternative choices by Mendeleev could work since they would fail to achieve this.