Not really. The Dagger will be a good secondary weapon for the few dex based characters, but almost no one will use it as their primary weapon.
The Hand Axe is good enough for most characters to use as a primary weapon, especially with Two Weapon Fighting, and I think only the Druid, Mage, and Monk don't have proficiency with it. Since the Monk will be fighting unarmed as their primary weapon, and the Mage should be using Cantrips, it's really only the Druid who's lacking. In our playtest the use of the Handaxe doubled once it was Simple at 1d6, and it's pretty much everyone's primary or secondary weapon.
That's kinda the point. The Martial weapon is in no way better, and is in fact WORSE than the Simple weapon because it's 4 gp more. You would think it would be the other way around...