Plan to expand bombing campaign in Syria stalls amid U.S.-Turkey disagreements
Once again, 'Western-backed' is a misnomer, when the White House says Assad's departure is an important goal their actions belie the claim, and as we'll see in the last paragraph quoted, at most they want just Assad to go so that his régime can be protected from revolution. The proposal to bomb ISIS north-east of Aleppo is presumably taking a long time because they want to make sure that nobody attacks Assad's forces while they are about it. 
"Turkish President Recep Tay­yip Erdogan “continues to have a different geographic priority,” a senior administration official said, and is still primarily focused on Aleppo and Syrian President Bashar al-Assad.
“We want to go after ISIL,” the official said, referring to the Islamic State.
Assad’s military surrounds, and regularly bombards from the air, Western-backed moderate opposition fighters and civilians in Aleppo, Syria’s second-largest city, in the northwest corner of the country.
Although the administration has called for a negotiated solution to the conflict between Assad and the moderate opposition, some U.S. partners question how that can be accomplished as long as Assad and his military remain relatively strong and the opposition is increasingly weak."