I don't think a "rule" applies to hp vs width of cut. I do think that a "rule" could apply if it considered band speed and width of cut. Each tooth needs to cut some amount of wood to avoid wearing out making powdered dust, making that happen through a wide cut takes quite a bit of force. Force x speed = power.
To Martin's point, wide cuts need high tension and work better with wide blades, both of which stress bearings, shafts and the frame. You may need to beef up the whole saw-head while you are making it wider.