Blunt weapons never were better against anything.
Weapons with higher cinetic energy were better at inflicting damage because, well, higher energy. But it had nothing to do with them being blunt, and in fact they were pretty much never blunt - maces were flanged, flails were spiked and so on. It's always about 1) higher energy and 2) smaller surface of impact.
Blunt is by definition the least efficient way to deal damage.
That works to an extent (as said, most maces had flanges, ribs, or other shallow projections, but concentrating damage onto a small area puts a lot of stress on the object doing the damage. Sharp objects tend to break, bend, or blunt when they hit another hard object. The limitations of metallurgy at the time dictated the development and use of weapons with enough material directly behind the point of impact to survive for multiple uses against armored opponents.
Consider that many swords of the period had a sharp edge and a blunt edge, the former to slice and dice those unarmored or lightly armored peasant masses, and the blunt side to crease or dent armor on the occasional better equipped opponent. In later medieval times, many Germanic sergeants carried maces, primarily to engage other armored knights, while the bulk of the formation carried swords for multi-purpose use. Sharp swords used against hard metal armor had a distressing tendency to notch or break, so even the sharp sides often had a rather steep taper from a fairly thick center. As metallurgy improved, blades got longer, thinner, and lighter with the same or greater durability.
Axes used a heavy lump of metal, widening out behind the sharp edge,.to provide strength, and a long handle to provide the leverage to generate momentum. The Roman gladius was most effective as a stabbing implement, with a thick diamond-shaped profile to the blade and a short taper to the point. Making it longer would have made it a lot heavier and slower, or else a lot weaker. Polearms were already coming into the forefront by the timeframe of M&B, which could generate sufficient momentum at the business end to damage even the heaviest armor one could reasonably carry, and firearms eventually took that a step further, putting an end to the dominance of the heavily armored mounted knight.
Swords should be "somewhat" effective against heavy armor, but not as effective as blunt weapons, which in turn should be significantly less effective against lightly armored or unarmored opponents. While "blunt" weapons were rarely "totally blunt", they still relied on mass and kinetic energy more than concentration of force. In practice, it wasn't entirely practical to make a weapon that was "too sharp" (and thereby too fragile) or "too blunt" (to the point where it didn't concentrate energy on a small enough point to defeat armor).