In a word: nihilism. In another: narcissism. Project Mayhem is indeed a trick, but it's one "Jack" plays on himself.

Consider that blowing up the headquarters buildings of credit card companies does not suffice to achieve, or even approach, the goal of wiping out debt. Offsite backups are a thing. It doesn't even impair the operation of the business all that much, because disaster-recovery plans and hot failover sites are also a thing. All told, Project Mayhem might have produced a period of as long as a whole weekend during which bank cards wouldn't work, and maybe not even that. But even if we're exceedingly charitable and assume they brought all the settlement systems down for a whole week, that doesn't materially affect debt held by credit customers, especially in light of the brief spending boom that'd almost certainly occur once people's cards started working again. So blowing up the HQ buildings is big, flashy, maybe a bit expensive for a variety of real estate insurance companies, and ultimately pointless.

And the way I read the character, Tyler Durden knows this is the case all along. The only person he really cares about selling on his line of bullshit is his own alter ego "Jack". Durden exists because "Jack" created him, and "Jack" created him because "Jack" wants convincing that he's not as meaningless, not as worthless, not as pointless, as he feels himself to be. Because he feels himself that way, he can't muster the emotional resources to do this work for himself, so he creates Tyler Durden to do it for him, and Durden does it very well. Creating a fringe political movement that blows things up is incidental, and occurs not because Durden thinks that's a thing worth doing in its own right - it's an open question whether Durden can even be considered to have agency or consciousness independent of "Jack" - but because it serves the purpose of convincing "Jack" that he has a purpose.

This is a problem someone else might solve by volunteering at a retirement home or joining a church or starting a family - or all of the above, perhaps - but "Jack"'s too much of a nihilist to really believe in anything outside himself, and too much of a narcissist to really buy into anything that doesn't center on himself. We see the former in his internal monologue, which the film helpfully externalizes for us, and the latter in his behavior at the various support groups he parasitizes in the first act. So "Jack" eventually invents Tyler Durden, and Tyler Durden invents Project Mayhem, and this pays off for "Jack" twice over: first when he finds himself to have become the barycenter of a movement that has people ready to kill and die to advance its goals, and then second when he decides it can't be borne and sets about to destroy it, thus becoming able to conceive of himself as a virtuous man struggling against all the odds - and, in "killing" Durden at the climax, eventually succeeding in that struggle. The property damage, like the existence of Project Mayhem in the first place, is incidental; the only meaning it has in the context of "Jack"'s evolving self-experience, and thus in the context of the film, is an indication of the extent to which it's necessary for "Jack" to go in order to bridge the gap between how he perceives himself and how he needs to perceive himself in order to tolerate his own existence.

Of course, one's experience of oneself is rarely static, and Palahniuk and Fincher are too skilled in their respective crafts for it to be mere coincidence that Fight Club ends when it does. It would perhaps be interesting to watch "Jack"'s tenuous grasp on life disintegrate completely, along with his circumstances, over the next several days following the climax of the film. But I doubt it would add all that much of appeal to the experience, or have a fingernail's chance of getting past the first test audience on which it was tried.