Here, i am considering mostly the bend formed by tying a lark's head around a lark's head tied in the other rope, but the easy to untie bend and several other bends follow this trend.
If there are collars tied around the standing part of the rope, then those collars may, in many cases, be pulled outwards to give slack in the rope and hence make it easy to untie. there could be a case where these collars are just an auxiliary part of another knot that will be hard to untie on it's own, but so long as they are not, the collars seem to be the means by which a knot is untied. now, a jamming mechanism may be ultimately responsible for the slack there, but based on how these two things are coupled, i would speculate that collars in the rope are part of the jamming mechanism or crucial to it's function. So, the best way i see to evaluate the roles collars play in looseness of a knot would be to see how they are related to jamming mechanisms.
So far, the most common jamming mechanism I can isolate is either trying to have the rope bend in two opposing directions as tension is placed on each strand, at least within the realm of knots that are generally considered good. This generally requires a collar to provide the rope with a strand to bend, or at least many knots that i have identified to jam like this have collars (bowline, zeplin knot, alpine butterfly, carrick bend), but doesn't always in cases like a glumpir knot. so, i don't know the topological correlation here, but i suspects something does exist still, as many of these knots do require a collar, and my counterexample, the glumpir, is often very difficult to untie.
Another jamming method is to try and rotate something that can't be rotated. A good example of a knot that binds like this is a whatknot. So far as i know, there is no particular correlation between this and having collars in the rope.
Another jamming method is to just pinch one strand really really hard. Most knots that are typically insecure will jam like this, and this just makes them a pain to untie. I question whether this is even considered jamming, but some knots, like an overhand on a byte as a loop, bind like this.
This is not a complete list, but it's just some observations of mine.