Maybe there's something I'm not getting, but surely missiles (which travel in a straight line) would be too easy for the enemy to shoot down?
Missiles don't travel in straight lines even today - they are too afraid of getting shot down. Air-to-air missiles don't have to mind this yet, but any missiles aimed at ships or surface installations have to know how to dodge and weave in order to reach their targets. Some surface vehicles are gaining the ability to shoot down unwary missiles, too, so an antitank round will have to learn these skills next...
Multiple use drones have many advantages over single use missiles in a space battle.
The problem with small craft (missiles, drones, crewed fighters) is that their weapons are also small. Today, small weapons can do damage against large targets. In Trek, this no longer is true: targets have shields, and we have yet to see a compact weapon that would perform as well as the large weapons installed aboard big starships.
So a fighter or a multi-use drone is at a disadvantage: having to share its payload between multiple weapons or other systems means it may end up being below the threshold of effectiveness altogether. A one-off missile can dedicate all of its payload to a weapon that may stand a chance of actually inflicting damage.