There is a big difference between "adding" color to an existing chord via extension, and "subtracting" from a chord by dropping notes. In classical harmony theory the 5th of a chord is considered unnecessary, and is often dropped from the V7 chord and the root doubled. Not always but often enough for it to be mentioned in every harmony book I have.
The concept of "root-less" chord may be taken out of context in many places. In a nut shell the ROOT identifies the chord. So if the root is missing the chord should not be considered by the name of the root. In some cases when looking at the movement of notes the root is not that relevant to the sound of the movement. A classic (classical) example is, again, V7. In the cadence V7 --> I the root of the V chord is the "common tone". It doesn't move. That doesn't mean it is not important, but it does not contribute to the 7-->8, 4-->3 movement that defines the sound of completion. Removing it leaves one with the diminished triad on the vii degree of the Maj scale of the Key. The movement works and is called the Leading tone resolution, viii(o) --> I.
The point is that, strictly speaking, removing the root did not create a rootless V7 chord, it created a viii chord and that is how it would be notated in a classical chord analysis. In functional harmony one might consider the viii(o) and the V7 as functionally the same since they serve the same purpose when moving to I but that is only one point of view. Out of this context the V7 no root is simply NOT a V7 any more.
If one wants to think of the viii(o) as a rootless minimalist version of the V7 that's fine, no one could stop that. But that's not to say that some players wouldn't think "boy, a leading tone resolution would sound great here". Whether you think of it as a rootless V7 or a viii is in part, a matter of brain washing. It depends on the school of thought you were trained in and subscribe to.
When it comes to playing extended chords on guitar this is a very useful device since you only have 6 strings and 4 fingers and you WILL necessarily need to sacrifice notes. The issue there might be one of convenience rather than music theory. Can you get (1) closed harmony, (2) moving in small intervals, and (3) get your fingers where they need to be quickly. These are some of the things a guitarist needs to worry about. For this reason we drop roots often. BUT, and this is a big but, I am not sure we think of those as "rootless" chords rather than suitable substitutions.