At level 4 for fighters/barbarians/paladins you get a dual attack. You can also shove as a bonus action every turn which can be fun. If you dual wield I believe your offhand attack is a bonus action (may just be rogues).Yeah the separate movement and action points sucks a bit as a melee. If you are already standing next to the enemy, you can still hit only once every turn.
Melee characters really start to feel more useful around levels 3/4