You can't board at long range.
Assuming boarding is necessary, and that you are willing to do it looking down the barrel of any weapon at all. I find it implausible that the desperate trader turned pirate you are citing is going to be equipped with specialist boarding equipment. They will need to rely on compliance and if that is happening then it doesn't matter what the defender is armed with, they had their chance to attack you before you got to boarding range.
As a pirate, unless you want to risk destroying everything you're trying to steal, you don't want to shoot unless you have to. So the quandary for the pirate is: shoot at medium range until you cripple the target (risky: you get no called shots)? Or don't shoot, and risk the substantial chance of the enemy taking you out of the fight with a single shot? It's not a theoretical issue of DMs: it's a practical issue of profit (and of not having the Imperium send out a flotilla to hunt you down, which the PoD Companion is very, very explicit is what will happen if you take that approach, really quite quickly).
Traditionally it has been strike your colours and surrender and shut down the power plant or we destroy you. If you comply a fast launch can be sent over with a boarding crew while the ship remains under the guns of the pirate standing off. You might destroy the launch (you can do that with a portable fusion gun) but it will seal your fate as the pirate will destroy you on principle.
The rest of your post assumes the worst possible roll for beams then the averages for missiles: this does seem like something of a concession!
Not really. I just don't conduct the fight where everything favours the beam weapon. Rolling 5 dice for damage is far more likely to result in something around the average than rolling a single dice. It's not just average damage to consider it's modal damage. That's just probability, the cahnce of you rolling minimum damage is 1 in 6, the chance of rolling minimum with 5 dice is 1 in over 7000. If you prefer we can say the beam weapon rolls average damage and gets 5.5+ effect. It might make 10% of a traders hull and cause a level 1 critical. It is unlikely to make 2 and it absolutely won't destroy the ship unless you get a 6+ critical and you need effect 8+ to cause the level 3 effect that spells instant disablement. If we say maximum damage 8+effect then you will get a sustained damage critical and likely a second one. I would get 30 and on a type A that would be 3 crits per missile at least and up to 11 crits total if all 3 hit.
Then you assume that the pirates attacked by missiles fail their point defence. This will happen one time in 36 at best. A mediocre gunner (skill 1, no dex DM) using a turret with 2 beams (leaving room for sand with the other) will make their point defence roll at a bonus of +6. That's with no fire control, no upgrades, no augmentations, no skill-chaining with the pilot and they are already automatically removing one missile even on the worst possible roll. Five times out of six they take out two of the three missiles. Roughly three times out of four they will take out all of the missiles. And that all
Regardless of the effectiveness of point defence you have still forfeited your attack for the turn. If I keep up the barrage as I try to evade that is 12 turns where you have no choice but to keep shooting down missiles rather than actually harm me. This frivolous waste of ammunition will cost me over MCr1 with advanced missiles, so the trader will need to decide if they can actually get away and whether it it is worth the cost. As they have no idea of the motivation or cruelty of the pirate that could be loss of all cargo, loss of the ship or spacing the entire crew.
This is only a factor if the pirate is armed with beam weapons. I would have assumed pulse lasers anyway. If they have gone for beams then I have even more time to escape you as you can't hurt me until you get to medium range. That could be hours. Why is a pirate optimising their weapons to point defence against an attack that you consider to be unlikley?
In which case great: they spot the laser turret and wisely sod off! No merchant will be able to stand up to Hroal Irontooth in the Meatgrinder, so the turret is moot for the extreme example of "we just wandered out into the notorious Trojan Reach and hoped for the best".
If they can stand off they might as well have a pop with their pulse laser if you didn't surrender and power off the plant as required. If they get the turret they can close and board, if they kill the plant they can close and board. It isn't the best outcome, but if you are that sort of pirate then maybe you don't care.
I prefer not to have that sort of pirate in my games as it makes it difficult to keep players alive. I want pirate encounters to be a challenge to overcome, not a succeed or the campaign is over proposition. In order of preference: 1) you run 2) you surrender (if the pirate is known and has a reputation of being merciful) or 3) you fight as a last resort.
If you choose 3 then you fight to the death as you have already assumed the pirate will not be merciful at option 2.
