Damage by Class instead of by Weapon

In my quest to simplify Dungeons and Dragons, we've arrived at the weapons system. I've transferred the source of a player's damage die from the kind of weapon they are holding to what class they are playing as. This way, players can choose whatever weapon they want without it negatively impacting their damage output.

Why and for whom?

There are two reasons why I wanted to make this. If you get the vibe I am trying to create, feel free to implement these rules into your own games.

• One of my groups is composed of people with varying work lives. This means that I can play only once every few months with those guys, sadly enough. And those guys tend to forget a lot of the more intricate rules of D&D that you simply learn by playing D&D more than once every 2 or 3 months. For them I wanted to go back to the basics, so they can lose themselves in both the social and the combat encounters without having to know exactly how to build a fighter that isn't accidentally weaker at fighting with a sword than the party's wizard.
• Additionally, as a player but also as a DM, I am very much in favor of flavor as the guiding force in my D&D games. As such, if a player comes to me and says: "I wan't to play a melee damage-dealing rogue, but I don't want to wield a rapier, but something that still does the same damage." I reply with "of course I'll allow that". And I give them an axe for instance, but with the exact same stats as that rapier.