If you don't overstuff your synthetic jacket or bake it to death in the dryer, it will last a long time. I wonder if the extra bulk of synthetic insulation encourages black-hole-infinity stowing techniques?
Trying a cheap one will get you into the same trouble that any cheap gear will: short service life and poor performance, leading you to decide that synthetic insulation is no good!
If I'm looking for insulation, I prefer the thicker stuff in the 100g range; otherwise I go to fleece. I like Patagonia Micro Puff, First Ascent Igniter, and REI Revelcloud on the thinner side. The Mountain Hardwear Compressor jackets layer well too.
BTW, they do make synthetic insulated garments with replaceable insulation: 3-in-1 jackets with zip-in fleece liners. Columbia made a number of 3-in-1 jackets with synthetic liners. But why not layer up with your UL windshirt or rain shell and have it all, when and where you want it? I can take a vest to use with my windshirt for backup on a summer day hike or step up to a sweater cut for colder weather. With these separate components, I can wear one, the other or both, and replace each as needed.
Buy a *good* jacket used or on sale. REI has the Revelcloud line on sale and 6pm.com is good for sale Patagonia stuff.