Here in California, we need 2x10 rafters to have enough depth for R-30 insulation, so the strength issue of the rafters is a moot point. We must add 2x10s. If your project doesn't have this (R-30) requirement, remember that, in most cases for conventional framing, the span of the roof rafter is reduced by purlin braces which will be removed. It is unlikely the typical 2x6 will span from ridge to bearing wall.
IMO, collar ties are Viagra for framers in that they assist in the erection of the roof framing before the roof sheathing is applied. If you modeled roof rafters with collar ties up near the ridge board, you would find the connection of the collar ties to the roof rafters to be impractical to detail or build.
Personally, I install the ridge beam below the existing ridge board. I face nail the existing rafters to the new 2x10s and connect the 2x10s to the new ridge beam.
Depending on the geometry, I have found the stiffness of the ridge beam is more important that its strength because, when the ridge beam deflects, the walls attached to the roof rafter bow outwards.