Of course dumbbells belong on that list as well, simply because they provide resistance too. However there are some reasons to look a little closer at what dumbbells bring to the table.
I will point out that some of the advantages or unique points to training with a dumbbell are also true of resistance bands or cable / pully machines.
For most schools though, a complete set of dumbbells will be a better investment than cable/pully machines as the machines tend to be focused on a single or only a very few movements.
Dumbbells and resistance bands are not limited in the same sense and offer a plethora of possibilities that more specific machines and modalities don't
Some advantages or unique properties of Dumbbells
Cost - Dumbbells typically cost less than barbells and plates which in turn cost less than machines. They are offer a lot of value for the schools athletic equipment budget.
Minimal other equipment required - Dumbbell's are often utilized standing and require nothing more than a space for the athlete to stand and have freedom of movement. Some dumbbell exercises require an adjustable weight bench. Even top quality adjustable benches are reasonably priced. An adjustable bench and protection for your floor assuming you don't have rubberized or similar flooring in your facility are all that are needed for exercises requiring a bench for exercises where it's difficult to place heavy dumbbells down gently.
Safety - No athlete will ever suffer a fatal injury from dumbbell bench presses by becoming pinned beneath the bar as there is no par coming down on the lifters chest. Unless you are doing an exercise that brings a dumbbell over your face, dumbbells are inherently safe.
Single Limb - Dumbbells are most commonly held one per hand. As such they can be used to train around injuries very well. An injured right shoulder need not hamper training the left when one is using dumbbells. There are numerous medical studies
Balance - Some times an athlete will have a stronger side. Lifting with Dumbbells will quickly make this apparent as the weaker side will lag the stronger when pulling or pressing.
Stabilization - Because dumbbells are held in each hand and there is not connection between them as in the case of a barbell, each limb is free to move independently of the other. This places more stress or activates more of the stabilizer musculature along the spine. Working these muscles will help the athlete to be more resistance to injury. In many sporting activities, forces act on one side of the body and not the other or at least not equally. The stabilization muscles help to absorb or counteract that force. It stands to reason that stronger stabilization muscles will make the athlete better prepared to handle those forces.
Fast Weight Changes - Assuming you have either a set of fixed weight dumbbells or selectorized dumbbells, it's very quick to change the weight for different exercises or sets if doing multiple sets. Dumbbells can be carried to another workout station and used to pre-exhaust a muscle group if desired as well.
Targeted - Dumbbells work great if you want to target an individual muscle with a simple movement whereas barbells tend to be more suited to compound movements. This is a great way to target a specific muscular deficiency.
Dumbbells also offer a nice change of pace for the athletes and help keep things fresh which has been shown to be important in training not only for the mental aspect of the athlete but also for the body and central nervous system.
If nothing else pick one barbell exercise per week and have your athletes work with the dumbbell equivalent and observe the athletes, their attitudes and outcomes. I think you will be pleasantly surprised.
Dumbbells offer many pluses and should be a part of any coaches repertoire. They are of good value to the school and the athlete alike. Their advantages in training effect and safety make it almost irresponsible not to be using them.
If you aren't using them today ask yourself why and look into the many advantages yourself and proceed accordingly.