All right so @Dmitry_Kashulin is claiming his future chances at finally acquiring a unicorn are at risk. I for one would never, ever deny anyone their shot at 
glory!
What if we scope it to just this for now:
When you add a Query (BAQ) to a dashboard your tab are: General, Publish, Filter
We are talking about adding an addition tab Parameters
it would look very much like the filter tab - except you cannot add or set columns here you simply see the list of BAQ parameters and you cannot control condition it is just equals.
You can then map that parameter to the same value options you have when setting the filter. If you leave it unmapped you get the prompt to enter the value like you do today.
If we go to size this and do, I want to keep the first pass simple. Every additional complexity layer adds significantly more cost and my goal is to keep this small enough that we might be able to just sneak it in one dark sprint. If it gets too big it goes into the ‘whose demands for the release get done’ scrum and past experience doesn’t bode well.
So if this basic set meets your needs, I’ll go grab a developer and get them to size it up for me.