Daggers and Scepters were a mistake.
Which is to say, they’ve sort of overshadowed the design scope of the other three melee weapon types. (Soon to be four, with spears!)
In terms of design, it’s a question better answered from the time before Daggers and Scepters. In this time, we had a paradigm that rather mirrored Fire, Lightning, and Cold Damage via Damage Spreads. More specifically, Axes and Fire Damage both had damage ranges that were fairly moderate, enabling decent highs without having too-punishing lows. Maces mirrored Lightning ranges, albeit to a lesser extent, with the highest damage ranges of the trio of weapon types, resulting in inconsistency but the highest average power. And Swords mirrored Cold Damage with the tightest damage ranges, making them very consistent. Swords were also the fast one, Maces the slow one, Axes the dead-average one.
The introduction of Daggers and Scepters, and the proliferation and importance of Conversion and monodamage builds overshadowed all of that minutiae. Nowadays the difference between Swords, Axes, and Maces is really just thematic/decided by whether you want a given Devotion constellation (of which, Sword is really the only good one of the three…)
With Physical conversion values being as low as they have been since Conversion was introduced as a mechanic in Early Access, and with the overproliferation of non-Physical bases, Physical base items are sort of inherently worse than all others except in either Physical or Pierce (with high AP%) builds. I wouldn’t argue their other stats necessarily make up for this, but maybe that’s the idea.
You can find some of my saltiest posts from the era in which Conversion + Daggers and Scepters were being added to the game. My salt may have receded since then, but my opinions haven’t, and over time I’ve only felt more vindicated with how things have turned out. 