If I remember correctly, the Helghast were actually the ones to start the major war on the ISA, under the leadership of the Scholar Visari. Hell they even nuked their own city near the end of the war so they're hardly what I'd call the good guys! I haven't played Shadowfall though so perhaps its changed a bit in the future. I agree though that they do look badass and have some sick melee animations in game!
The Helghast (Not original name) and ISA were once one group, but the group disagreed on things and eventually broke into two groups. The Helghast went to colonize Vekta, a beautiful lust planet, very similar to Earth. The Helghast set up trade routes, but to keep it safe, they had a tax on it. There was other routes but they had asteroids and pirates. The ISA didn't want to pay the tax, they wanted to go for free. After some time, the ISA pretty much ran Earth dry, so they needed a new place to live. The Helghast refused to take the ISA refugees, for a couple reasons 1) fear of a repeat of early disagreements 2) what happened to Earth would happen to Vekta.
This PO ISA, who then invaded and kicked out the Helghast, who out of desperation colonized the planet Helgan. Helgan had poisonous gas that killed many Helghast, but changed many others and future generations. Due to the gas, most lost their hair, as well caused their skin and eyes to look sickly. The Helghast (think ISA gave them this name as mockery for living on Helgan) wanted to take back Vekta from the ISA. The ISA cried that there was women and children on Vekta, and was an act of war. However, the Helghast didn't care because there was once Helghast women and children on Vekta. The Helghast wanted the ISA to suffer like they had to.
As for the bombing of the Helgan city in KZ2, it wasn't an easy choice or else Visari would of blew it up the second you landed. It was an act of desperation, because the Helghast were losing the war and the ISA military was all over the city. So it was an unfortunate necessity, to weaken the ISA forces. The ISA did a dirty tactic and brought the war to the city, thinking the Helghast were gutless, and would run and not attack the city causing them to surrender. It didn't work like that, and it cost both greatly. If the war took place say out in a desert, the ISA invaders would of been nuked on the spot. Visari just wanted Vekta returned to the Helghast. The Helghast were not without honor, Col. Mael Radic respected Jan Templar so much he was very disappointed he had to kill him outside the battlefield.