Having had some time to reflect since I originally posted the question, I can see three appeals of the damper:
1. It's lightweight. While it may have the same *volume* as a turret, its mass is less, and that means that there's less thrust required from the manoeuvre drive to support it, which implies a smaller manoeuvre drive, and (more importantly from a volume perspective, less fuel to be carried).
2. It needs less crew. For a group of lasers to target separate missiles, they need individual crew (an MFD can only direct them against one target). In contrast, an MFD can direct a group of Nuclear Dampers (just like it can direct multiple missiles separately) and therefore one crew member can (usefully) man multiple Nuclear Dampers. Again, this means they have a smaller footprint on the ship.
3. [This is slightly lawyerly] In Battle Rider, Nuclear Dampers are described as being targeted at missiles that survive laser fire. If one interprets this rule in favour of the dampers (and they could use a bit of favour!) then dampers can ignore missiles that have already been hit. This can make them useful as a second line of defence. E.g. you have 20 lasers, and 10 missiles coming in; 2 lasers have a shot at each missile, if they both miss, you're in trouble. Alternatively, you have 10 lasers and 10 NDs; 1 laser shoots at each missile, and you allocate your 10 NDs at the survivors, if 5 survive your lasers, then you put 2NDs on to each of them.