One of the problems would be the size of the diffraction limited field. Even
in an f/5, this area is very small. The paracorrs correct a lot of this but
not all. If you look in a f/4 you will see a very comatic field using standard
oculars and no coma corrector. A bigger scope (by virture of its size) shows a
smaller true field of view. If you want good definition and contrast on an
extended object, that will be very hard to accomplish. Also, the bigger
aperture, the harder it would be to meet its resolution criterion unless you
have a fabulous figure...and, again, the size of that field is extremely small.
Many years ago I spent some time panning with a 10" f/4 Newtonian (expensive)
richest field telescope. I used several eyepieces and could not believe the
extremely comatic images and light scatter. This may have been a poor example
but I was shocked.

About 25 years ago, I had the pleasure of meeting John Dobson. I spent most of
an evening with him up at Mt. Rainier. He mentioned that he thought parabolas
of short focal length were very lacking visually. At that time, he felt
anything less than f/6 was questionable. I don't know how he feels now. But I
do believe he was (and is) an authority on Dobs!

Maybe the thing to do is talk to someone about making a Ross corrector
(paracorr type) specific to an f/3. Richard Suiter could probably point you in
the right direction regarding ray tracing. I think best case you would end up
with a lot of optical aberrations...and that secondary mirror minor axis would
be pretty darn big-and the mirror expensive to boot!