The best way I'd summarize how BSR works with respect to mixed attackers is that a mixed attacker like Infernape isn't a better physical attacker relative to a purely physical attacker like Machmp merely because Infernape can also run special or mixed sets. In terms of their Physical Sweepiness component, the two mons are just evaluated based on Speed and Attack. Special Attack/the ability to go mixed just isn't factored into PS.
In terms of how the final BSR is calculated from PS, PT, SS, and ST, it's not literally just PS + PT + SS + ST, but it's not that far off from that. So, yes, being better at both Physical and Special sweeping will result in a higher BSR than being good at just Physical sweeping alone, even if the Pokemon will only ever run physically attacking sets.
This does mean that Beartic comes out ahead of Golurk in BSR in at least some part due to its higher SS stat, even though neither Golurk nor Beartic will ever be using special attacks. If I assign Beartic the same SS as Golurk, then the BSR gap between the two mons drops to 7 points from the actual 15. So about half of the BSR difference here comes from a special sweepiness rating that will never matter, while the other half comes from Beartic's greater bulk.
The fact that Beartic is rewarded like this for a SpA stat it will never use is perhaps not ideal. But the point of BSR is really just to look at stats in a vacuum and in that sense, Beartic really is a more viable special attacker than Golurk is, and the BSR reflects that.
IMO this doesn't mean that BSR is wrong. It really just comes down to the fact that BSR isn't the end-all be-all. It evaluates stats in a vacuum and you then have to look at them with added context of the Pokemon/metagame.
For example, Beartic is ostensibly bulkier than Golurk due to a higher HP base stat of 95 vs 89 and the PT and ST stats reflect that. Yet no one would ever use Beartic defensively in any metagame due to its Ice typing and the many weaknesses that come with that, including to Stealth Rock, as well as its lack of a support movepool that would make a defensive set worthwhile. Golurk on the other hand has a good defensive typing with 3 immunities, as well as Stealth Rock, which in some metagames has led to it being used as a bulky SR setter.
Similarly, if you look at the BSR, you'd say Dragapult is a better physical attacker than special attacker, but we know it usually isn't, and that's because of movepool.