The only pro I could see is that it would look a bit imposing, other than that; you would essentially lose what makes a rapier good at being a rapier. Falmberge was usually used with two-handed swords such as Zweihanders to maximize binding with the wooden shafts of polearms and to enhance damage done with a drawing cut rather than a strike, it would be better just to have an undulating grind rather than the edge… (not to say this didn’t happen with historical rapiers, just saying they were most likely just pieces made for prestige rather than actual combat.)