[Gravityloss]

Some good points from first principles. But there are ways. If you manage to make the composite with a very good process so the fibers are straight and closely packed, then it can have good compression strength as well.

This can be achieved for example in pultruded carbon rods, where the carbon fiber is under tension when it passes through an epoxy bath. They have been used in aircraft wing top spars which receive compression loads (when taking positive gees).

How to make a cylindrical vessel that can take compressive loads? The creation process certainly needs some thinking and attention.

[Gravityloss]

Thinking about this more from first principles, if I got it right, the cylinder hoop stress is twice the longitudinal stress. So you could pultrude a unidirectional layer of hoops, or very shallow angle spiral to handle half of the the hoop stress only on the outside. Have normal cross wrapping layer on the inside probably.