The concern with having the clay trap in your kitchen sink is that everything else will wash into it too - food scraps and soaps and everything. You will get a stinky, fermenting mess really fast. If you put a clay trap in your kitchen sink you would need to empty and rinse it every day... and then there is the issue of finding a suitable place to dump out this stinky clay-food combo every day.
In my first studio, there was not a sink I could use for clay. So in my back yard I put a laundry tub hooked up to a garden hose, with a 5 gallon bucket underneath to catch clay chunks. I had only cold water and it was only any good until the winter, when it became too cold to use any longer. But it was better than nothing!
Eventually I moved studios, and now have a large basin sink I can use for clay tools (and the warm water is so glorious!). I built my own clay trap from two nested buckets. It's quite straightforward and I feel confident that if I can do it, anyone can do it
If you only have a kitchen sink to work with, the dishpan method might be best. When I do pottery at a location without a trap, I set up several 5 gal buckets of water and we wash all clay-covered hands & tools in there, then dump it outside afterwards.
Gleco works for me. It is relatively easy to install and cleaning out the trap is a breeze (albeit a 'stinky' breeze).
I laughed out loud at this. So true!