I would first say that it gets mixed up with the school walk now.
They are not well defined… and theories surrounding the different types of walk are subject to great discussions… 
Maybe someone more versed in classical riding will chime in and disagree with me, but to me :
A school walk is closer to the spanish walk
A counted walk is closer to the piaffe.
In the past: The counted walk was really diagonalized and the school walk wasn’t.
Now: You don’t want the walk to get lateral.
So the counted walk shouldn’t be 2 beat, but it does get close since the next step can be the half steps/piaffe.
If the OP was consciously asking for this gait, the horse would be doing what could be considered kind of a mix between the school walk (more suspension) and the counted walk (slower- closer to a lateral walk without being it).
It’s more of the French tradition. You can find writings from German riders too.
If you can get your hands on Oliveira, Beudant or Henriquet books, those would be great readings to start. I find Philippe Karl to exagerate with his hands… but that’s just me.
*My books are all in French and today, my English brain is still on vacation.
To me, despite the tension that can occur (and should be « eliminated »), it is a great tool to work the horse’s shoulders and develop the hind leg thrust/engagement.
It makes horses more expressive and mobile. (You get to control its legs quite independently)
I really see nothing wrong with playing with what the horse is willingly giving. It broadens its range of motion and develops more refine movements (? moving more graciously).
And yes, again, negative tensions in whatever you are doing should be diffused into positive ones.