There are however some people out there who think that BPSS is a “must tick” box for everyone.
These people have probably misunderstood (at some level in the chain) the message from above. As you rightly say - an SC or DV checks the same information and more.
Fortunately, there has been some recent clarification which clearly states that those with a current security clearance are not required to go through BPSS.
(Though, I won’t be surprised to find that people are still pushing for it… I’ve already heard of one person be told that their DV isn’t acceptable because “it’s not through the MOD”. That’s absolute nonsense. DV is DV.)