You will note that those documents have almost no mention of leakage. The leakage characteristics of polymer caps is still an issue. In applications like power supplies it can be ignored, but definitely not in timing circuits.
I'm not saying that polymer caps aren't good, they have some amazing characteristics, but there are still cases where you would choose a ceramic or a tantalum, it even a regular electrolytic over them.
Will they improve? Sure. Nobody uses waxed paper capacitors any more; once upon a time they were the go-to capacitor. As polymer caps improve, maybe regular electrolytics will be the next capacitor to go the way of the dodo.
And you seem to have film capacitors wrong in your head too. There are many types of film capacitor, if you want the best in stability, leakage, any temperature performance, you'll probably end up with a film capacitor. Years ago you would have chosen mica. These days we have plastics which perform similarly and which are far easier to handle.
I just happen to have been looking at a design where polymer caps might be a very good option, so I've been reading datasheets and doing comparasons
Oh, one other thing, at the moment the polymer caps can also be more expensive than some alternatives, although it looks like that difference is reducing.
Another really weird thing is that surface mount polymer capacitors have significantly worse ESR characteristics than through hole equivalents. I'd love to know why that is the case. (It's especially weird given that the metal can type SMD devices are not that much different to their through hole cousins.)