If an extremist group didn’t commit heinous acts, they wouldn’t be much of an extremist group, would they? They’d basically be a bunch of loons waving guns around on YouTube.
To some degree, there is self-selection going on. The extremist groups that don’t commit huge, newsworthy acts just don’t get enough attention to get much traction. It’s pretty satisfying to fight the US. It’s much less satisfying if they only people fighting you is the local school board. There are probably plenty of Islamic extremists who content themselves with writing diatribes and having heated dinner party conversation, but we don’t really pay any attention to them, because…who really cares? And they don’t get a ton of recruitment, because there is no real narrative arc to what they are trying to do.
So those that do commit atrocities-- what is the motivation? A big one is just provoking enough attention to gain some credibility. If national and international forces are concerned with you, you’ve instantly got a lot of street cred. And if you those big, often unpopular, concerns do things that can be spun as unfair or atrocious, then you’ve got even more credibility. If you were a budding gang member, would you rather join the Crips or would you rather join the up-and-coming 39th and J Bad Boys, best known for once robbing 3 entire cases of Budwisser from the local 7-11?
These guys are playing with relatively few cards. They can easily raise an army of unemployed young men, but that army will not be particularly loyal and will expect to get paid in ways that may not be easy to sustain. They cannot win a fair fight, but they can make terroristic strikes. They probably cannot reach the most serious targets-- things like government buildings or military installations. They pretty much have to focus on non-secure, non-sensitive locations. They are limited in their ability to collect taxes or provide government servcices- somethign ISIS is trying to jump on quickly but will almost certainly face real challenges with. They can raise ideological fervor, but that carries a risk of factions and in-fighting and other messy realities- as well as the envetuallity that there will be conflict between strategy and ideology.
Now and then it’s worked, but not all that often. Established powers get all of the good moves.