Devil or angel?
Thank you so much for starting this conversation! I think the term sucker is a bad name for an advantageous shoot and automaticly implies a negative connotation as an evil weed to what can be a very useful tool. I consider them gift from the tree if you're looking to increase your stock.
I'm very glad to see you join the conversation Bob, you've pulled my bacon out of the fire on a number of occasions. I have great repect for your wisdom and much appreciation for your helpfulness. You've been a guiding light in my dark journey of self-teaching.

I have to spit things out to hear what I'm thinking sometimes and I have some ideas and practices on this subject.
I think it depends on what type of tree, what you want to do and where you are at with the tree or where the tree is at in it's stage of development.
Pyrocantha is one that comes to mind that suckers so profusely as to be disasterous to itself and surrounds if not cut, what, two three time a season. Made the mistake of planting aspen in the garden! I won't do that again unless it's in a deep walled container or I've thought of one of those kids swimming pools buried in the ground. Talk about suckering!
I have been using these tools in my own experiments. I think there is a symbiotic relation between the tree and its offspring. They do not rob each other, they feed each other. I think the Quacking Aspen defines this better than any tree.
Learning tool- I have an English Elm I've grown from a seedling and beginning to shapeup. I've been reading about the hedge trimming method and wanted to try it out, but not on my baby. I've let a few root suckers come up about a foot from the tree and have been practicing the hedge trimming on them. Actually developing nicely into a small tree. As I grew these shoots out I noticed that the vigor on the main tree was also increasing, doubleing the number of advantageous shoots and extentions. This elm has been my whipping boy and I've knocked it back pretty good a few times, it's a real trooper.
I have over the years allowed shoots to grow to several feet before removing them and it really pumps up a tree fast both in root mass and trunk size. The elm is/was a bit of a spindle and I've thought of airlayering below the lowest branch, but rather I'm letting shoots grow around the lower trunk areas to see if I can put some bulges into it. I can always airlayer, but in time I think it will work out.
I have a large English Hawthorn I am going to airlayer. I have ground and I like trees that I'm growing out for future work to have full advantage so in the ground they go. Especially if they are weak and ailing, nothing brings a tree around like a couple of seasons with mama.
Talk about another profuse producer! Four years running I've gathered about ten good starts from this tree. The first are now pushing an inch and a half and making shoots of their own. Note that I've kept the suckers off of this tree. It has a nice root base and I want to take three airlayers from the top so I've been pushing all the energy up there. I let the root suckers get about four to six feet and take them like a heel cutting and shove them right back into the ground. I get ten bucks a pop for them the second year! Better than a poke in the eye, which this tree is notiorious for.
That's my thoughts, I'd love to hear yours, Rick