That just induces a sideslip which doesn't get you into clear air any sooner than just applying forward cyclic....
Exactly the same result would be achieved if you just pulled power at the incipient stage without any of the sideslip
Though I'd have to defer to your doubtless greater knowledge and experience, I believe that the pedal opposing the cyclic allows the additional translating force of the tail rotor to assist with moving out of the VRS sideways, whereas forward cyclic alone has no such benefit, and would rely solely on the result of cyclic, ie. main rotor vectored thrust only.
As for sideslip. I'm not sure I understand your point, as that would only apply in flight with significant forward (air)speed, whereas in this case, by definition, there's negligible horizontal speed. So it seems the technique is designed to use every means possible in order to translate out of the VRS ASAP, which undoubtedly is swifter with the assistance of the tail rotor thrust.
But I'll be happy to be corrected if I've missed something obvious in your reasoning.