To anyone asking, trash bins are working but they are relatively slow.
By default the small bins clean every 2000 ticks, the large ones clean every 1500 ticks (at speed 3 your game runs at 360 ticks/s max, at speed 1 it's 60 ticks/s).
If you have a lot of filth, it takes a long time, it does clean stacks of filth if they were dropped all at once but otherwise it scans the area and cleans the oldest filth first, if your pawns are dropping filth on top of filth you might not see it getting cleaned because it cleaned the ones under it.

If you want to make this faster you can stack bins or you can edit the XML file that controls the speed:
Inside \1.4\Defs\Buildings_Misc.xml
Search for Bin_Large and Bin_Small and edit the "<timerInTicks>XXX</timerInTicks>" fields to be faster.

Here's a video of filth cleaning at speed 3 with that field set to 10 ticks: https://streamable.com/pa3kxd
You can see towards the end that new filth is being dropped but it's only being cleaned after older filth is cleaned first.