I think this is more an issue of 'small energy weapons are extremely mediocre' rather than 'Burst PD is terrible'
What are the similar weapons in the Small Energy slot? PD Laser, LR PD Laser, Tactical Laser, Mining Laser (I'd argue that IR Pulse, Antimatter, and Ion Cannons are all quite different, and I'm not going to talk about them until the end).
Mining Laser is practically useless. 600 range, which is more than the PD laser, but only 30 DPS makes it ineffective at stopping all but the worst missiles, and completely ineffective at anything with armor.
PD Laser (4 OP) offers 75 DPS, but short (400) range usually means that it will not be able to intercept many missiles without a lot of overlapping fire. Salamanders can be quite problematic if you are relying on a PD laser to shoot it down.
LR PD Laser (5 OP) only has 50 DPS, but a slightly lower flux cost and twice the range (800).
Tactical Laser (4 OP) has 75 DPS and long (1000) range, but has a 1:1 flux cost and requires the IPDAI to function as anti-missile PD. It also doesn't have the fastest turret traversal, meaning it can struggle to hit a salamander or fighter with a high radial velocity.
Burst PD Laser (7 OP) has 64 DPS under sustained fire, so more than a LR PD Laser, but also suffers from short (500) range like the PD laser. However, the higher burst damage can help pierce any armor on a fighter, and it has high initial DPS with the 3 charges to potentially delete a fighter wing.
Basically, my thoughts are as follows:
Mining lasers aren't worth it.
PD Lasers are good at dealing with harassing fighters, but aren't great at shooting down missiles before they impact your ship.
LR PD Lasers are good at dealing with missiles, but lack the DPS to kill fighters particularly quickly.
Tactical Lasers require a specific setup (and therefore extra OP) to deal with missiles, but are quite effective vs fighters if they aren't swarming you.
Burst PD Lasers offer a mix of ability to defend vs missiles and fighters, but only offers solid protection for a very limited time. Therefore, it struggles against a lot of pressure systems like Annihilators or Squalls, or heavy fighter strikes such as strikes involving a Khopesh Wing, or even a Piranha Wing. That said, they struggle against Broadswords due to the flares
For me, I go with Burst PD on most larger ships, as if you need better screening, you have escorts.
The other small weapons are all somewhat specialized (IR Pulse laser for hard flux DPS, AM Blaster for burst, Ion for EMP)
I do use HBLs on Astrals as they are not good as a frontline carrier, despite the Advanced Optics, and the alternative is to put Burst PDs. HBLs are quite underwhelming in most cases, especially compared to the ballistic counterpart of Dual Flak (or even Flak).