Muralitheran is a chucker, and so was Shoaib Akhtar.
The ICC were blackmailed by the powerful Asian Sub-continent bloc into changing the Laws to allow both to continue playing.
And if you don't believe you can get more spin by straightening your arm on delivery, just try it.
I am just Joe-average when it comes to spin bowling, but even I can get a cricket ball to spin up to 50% more than a "normal" delivery by straightening a bent arm. If you do play cricket, try it next time you are doing "throw-downs" for a team mate.
Also, you get a LOT more control when throwing rather than bowling, and if nothing else, spin bowling is about control.
Try tossing darts at a dart board with a cricket type bowling action, and compare that with how you do at throwing them.
Try pitching the ball on the popping crease in line with the stumps from 20 yards with a bowling action, and see how many times and how close you can get to hitting it. Then try throwing the ball at the crease, and see how much more often you hit it or how much closer you get.