Drywall – How to install the plastic/nylon toggle anchors

Plastic anchors come in different quality flavors and having the collar or not doesn't correlate with that.

I use a locally manufactured (I'm outside of US) series of anchors without a collar - their diameter is slightly smaller than that of the hole and they have small relief dots extending from the surface so that the outer diameter is slightly bigger that that of the hole. They require some force to be driven into the hole - either pushing them with a hard tool or gently hammering with a hammer. My experience with these anchors is very good - they almost never slip given the material is hard and doesn't crumble while drilling.

At the same time I saw a lot of anchors both with or without collar that slip in the hole. So I'm pretty sure it's not the collar itself that matters.

That said another very important factor is how precise the hole is drilled. It has to be of exactly the required diameter. Drilling must be performed in such manner that the drill bit doesn't exert side load onto the hole walls - otherwise the hole is milled and the anchor won't hold there.

Also usual plastic anchors can only be used in strong solid materials that don't crumble while drilling. There're special "hollows anchors" (not sure of the exact term) that can be used for slightly bigger holes and for hollow materials - they tight into a knot when inside a hollow.

Finally the anchor diameter must be properly selected depending on the screw diameter. Otherwise you're screwed.

II would say you are fine (and you may have been fine before, who knows). You have replaced the screws that hold the cabinets to the studs, and those are the ones that hold the cabinets up. The ones in the face just keep the faces flush, so if one ever breaks, do the repair then. Hope this helps.