A better question might be what right the US has to be in Syria in the first place. I'm also not sure what gives you the impression that Syria is interested in such a conflict. The recent rapid moves by the SAA haven't been against US positions, they've been aimed towards establishing a solid land route to Iraq, allowing Iranians and Iraqi reinforcements to enter Syria without having to be flown in (like they have been in the past). In the meantime the US has been desperately and actively trying to prevent the Syrian government from regaining control of it's own eastern provinces, hoping to use the SDF and the NSA as a buffer between Syria and Iraq, making it a lot harder for the Iranians to move troops and supplies into Syria.
What's even more interesting is that Russia has significantly less interest (objectively speaking) in this arrangement. Russia's primary supply line is sea and air, and has been for nearly two years.