Hello Joly0
That's correct ... it was done like this when Cortana ans search was merged inside one component (removing one broke the other) , especially for taskbar search. But as MS separated Cortana and Search, and this is for the best obviously, there is no reason to keep this association like this.
So, you may consider your request as implemented in v2.3.6.1 [VIP] and v2.3.7.0 {ALL].
Thanks for the idea