The "bundle of sticks" analogy has historically been used a lot by fascists. If someone used it to try to convince me, you can be sure it would backfire!
I'm not sure it is great, to me it seems to handily encapsulate the bad parts of authoritarian ideologies. It's a demand to follow the will of the group, and to prioritize your group identity in order to accumulate power for that group. Whether that group is race, nationality, or economic class, to think of yourself primarily as an instrumental component of it is an abdication of responsibility to have and apply your own unique perspective and thoughts, and leads naturally to abuses by whoever happens to be doing the thinking for all these people who have chosen loyalty over agency.
Which isn't to say that cooperation isn't important and necessary to accomplishing any goal, but if this sort of group unity is the core idea it seems extremely dangerous and malignant.
It isn't that the words are scary that they should be avoided, it is that so few People bothered to learn what any of them actually are. And based upon the childish proclamation you made, I'm including you in the can't be bothered crowd.
It's important to be able to spread ideas if you want to see them succeed. So we could refuse to talk to people until they learn the words we like, or we could get creative with transmitting the ideas.