The structural damage you inflict in Guerrilla is permanent, as noted in Destructive Savior on the main page. In the Origins film, a primary problem the Red Faction now faces as the rulers of Mars is a lack of efficient infrastructure. Now whose fault might that be?
That's not what infrastructure means. Infrastructure is the most basic framework of a system, not physical structure. It is most likely referring to the organization of the Red Faction, which worked well enough for a resistance group, but does not have the organizational capability to run the entire Mars colony as a government.
Many High-Importance targets are key pieces of civilian infrastructure being co-opted by the EDF, such as the Ark power plant in Oasis, Tharsis Point Wind Farm and the Town Hall in Dust, and Harrington Memorial Bridge in the Badlands. Many others could have been converted to civilian or economic infrastructure if captured intact, such as the EDF Executive Housing and the entire strip mine complex in Dust, the Ore Processing Plant in Parker, or the Convoy Dispatch Station in Oasis, but they were destroyed.
Alec Mason is able to smash down buildings with a sledgehammer because he's new to Mars. He grew up under Earth gravity, the buildings are designed to stand up in Martian gravity, which is a third of that of Earth. He is, literally, superhuman by martian standards.
Because the alternative, to what was left of the Red Faction leadership, was submitting to the most powerful warship in humankind's history and an admiral who has shown no brooking for mercy. At least this way, the EDF will have no ability to militarily force the Martian settlements to come under their aegis. War is hell.