You might actually need 2x8 rafters in such a case.
Removing roof collar ties.
Collar ties are generally for the benefit of the rafters though and your rafters sound more than big enough.
An exception occurs however even near the ridge if the bottom of the roof triangle is not secured against stretching or flattening by a ceiling joist or a low placed rafter tie.
Collar ties are the appendix of roof framing an evolutionary dead end in home building hanging on by just a couple of nail points.
Watch this video before.
Well unless your roof is concrete tile and less than 3 12 in slope.
2x4 collars yes i use a piece of 2x4 placed immediately under the existing ridge like a collar tie but all the way to the top on each pair of rafters.
It ties the entire roof together.
So the top of the roof is in compression and collar ties near the upper roof should also be in compression not in tension.
The one in the middle is around 3ft height which results in an awkward limbo or high jump.
The only time collar ties do any good is when they are specifically designed to be functional by an engineer or architect and are installed with meticulous care by the framer according to detailed drawings.