You guys would have been thrown out of my old theory classes

Perfect fifth ..least important, not by a long shot..

The perfect fifth of the chord is your passing and lead in harmonics to the next chord.. Total emptiness.. There are no least important.. every harmonic that is added is important.

I would argue dropping the root would be better

no root = no definition. No identify. Ambiguous. Yes, all tones contribute, but the 3rd is more necessary to define a chord than a 5th. Bass players need/love the 5ths, and they should avoid doubling roots and thirds.

The 5th does nothing to define the "color" of the chord. It reinforces the fundamental but does nothing to denote Maj/Min. It provides added power, and strength to a chord, but with no 3rd, you have no key tonality. The Root, 3rd and 7th define the nature of a chord. The added "color" tones (2nds, 4ths, 6ths) provide more detail, and tension. In practice the Root and 5th work together to reinforce the overall tonality that is defined by the 3rd and 7th.

I wouldn't say that it's a case of more, or less important, as much as it is not as necessary in naming or defining a chord. Take organ stops as an example - the first 3 drawbars are 1-5-1, and used together, they sound like a solid tonic.

This is the book I bought:

https://www.youtube.com/watch?v=-Uqrbu-Z4y8