Your thinking is too clever by half. Like your Israeli example showed, you don’t need chemical weapons to get people to leave. Gun down all the adult men, rape the women and children. People will get the message and leave. Starvation is an even more effective tool to precipitate large scale population transfers. Immediate hunger and thirst will force undesirable Sunnis out of Syria faster than a random once a year chemical weapon attack.
The biggest problem with the American strategy in Syria is fundamentally because the Americans demand that they be the “goodies” and other people be “baddies” and thus the mountain of lies peddled by the American luggenpresse regarding America’s role in Syria.
The most beneficent reading of America’s intention in Syria is that the CIA/Pentagon/State Department honestly thought a foreign Jihadi backed Sunni radical movement could affect a relatively quick and painless regime change to a more Pro-American government and that simple bureaucratic inertia kept with this strategy for years past its sell by date even when it became obvious it wasn’t going to work. This is plausible because the American establishment is precisely that combination of delusionally stupid and cravenly careerist that this is a realistic explanation.
The alternative hypothesis is that the CIA/Pentagon/State Department knew exactly what it was doing in funding Jihadists and forming an alliance of opportunity with Al Qaeda and really has no expectation of actually overthrowing Assad. The entire purpose of the War is only tangentially related to Syria and it is instead primarily a method to bleed Iran and to a lesser degree Russia of men and material at relatively modest financial cost to itself. Afghanistan redux. The hundreds of thousands of Syrian dead are simply irrelevant roadkill in this strategy.
The rather bold faced lies coming from American state media could be reconciled by either explanation. The first theory is that the lies are to shield their gross incompetence. The second theory is that the lies are to shield their Machiavellian scheming which soft hearted American voters wanting to be the good guys would never publically approve of.