How about creating a bogeyman and an excuse to take part in yet another misguided military misadventure? We've destroyed Iraq, Libya and Afghanistan. Why should Syria be any different?
You think the UK and US governments were looking to get involved in another MENA quagmire? Seriously? The staggering cost, the (completely deserved) destruction of Bush and Blair's reputations, the deaths of thousands of their own military personnel and civilians, the constant threat to domestic security, the way that it shredded the legal and diplomatic basis of the post-Cold War international order making possible things like Russia's annexation of Crimea and making Europe less secure than at any time for 30 years - you think that the senior members of the armed forces and Obama and Cameron looked at all that and thought "yes, more of that, that's what I'd like to be remembered for, getting sucked in to a Saudi/Iran proxy war"?
If that were the case then there would have been a significant attempt at an intervention in Syria three years ago. Instead, Western governments practically bit Sergei Lavrov's hand off when he held out the offer of a compromise deal on Syria. Quite a lot of analysts were suggesting in 2012 that if Russia really wanted to screw up the US and UK, they could just stop vetoing US/UK attempts to push an intervention-favouring Syria resolution through the UN Security Council and watch Obama and Cameron embarass themselves trying to wriggle out of actually doing anything on Syria.
Obama and Cameron are not George W. Bush and Blair (Obama is more like Bush senior on foriegn policy than Bush junior), but I'd bet my house that even Bush and Blair wouldn't choose to send troops into Syria after Afghanistan, Iraq, and Libya.