Drywall – Threaded hollow wall anchors spin out partway in

An alternative to using a large wall anchor for heavy duty mounting is to always find a wall stud for whatever item you are hanging on the wall. Then you can use a smaller gauge screw (or nail) without any type of anchor required. This will leave a smaller hole in the drywall and give you all the strength you need, but limit you to the places where you can position the item.

I am not sure what the weight of the item is that you are looking to hang on the wall but another alternative could be to just use drywall screws without any wall anchor. In my house I do this a lot with light pictures, etc. A drywall screw positioned at a slight downward angle has a good amount of holding power especially if it is something that is not going to get a lot of use but just sit there (I do not recommend just a drywall screw for something like a coat hook).

And then you can always use picture hangers like this that would only make a small nail hole:

Or even those sticky Picture Hanging Strips like this:

It sounds like you want to keep using the existing holes, which by now are quite stripped and loose.

As mentioned in the comments, for a shelf you almost certainly want to fasten it to studs. However it is possible (though not advisable) to have a shallow, light shelf supported by drywall.

So if you are unwilling to mount to studs, consider using heavier-duty Toggle bolts as they stronger are not affected by a warn-out drywall hole. The bolts you linked are one of the weaker kinds and seem to rely on a snug fit. There are even more advanced versions, like the Snaptoggle that boast impressive strength, but most people remain skeptical about those claims.

No matter what fastener you are using, you are ultimately limited by the strength of your drywall. Thicker drywall is stronger, but all drywall will age and weaken over time. A shelf that feels sturdy to begin with may weigh on the drywall and cause it to sag over 10 - 20 years. Environmental factors such as the amount of vibration (from minor Earthquakes or from heavy truck or train traffic near by) will affect the rate of deterioration.