I think the confusion about tensile strength comes from imagining a single carbon fibre. It very obviously has little strength in compression, like a bicycle spoke. But the fibres don't act alone.

Even under tension, you need the epoxy to transmit loads between fibres, or else the carbon fibre is pretty useless which is why the finished material CFRP (carbon fibre reinforced plastic) is used. Unlike metals which are generally equal strength in compression and tension, CFRP is roughly half as strong in compression. But it's very light so from a strength point of view it's not automatically the worst material choice. I get Cameron's point but if it really had "no strength in external compression" then it would be a useless material in general.

Regardless of material the main failure mode of a tube with external pressure is buckling, so the strength in compression is much lower than what you expect from a hand calculation that doesn't consider buckling anyway[1]. But CFRP is a risky choice for at least 4 reasons: analysis is not as straight-forward/easy-to-trust, signs of fatigue are harder to detect, delamination is difficult to control[2], and interface to other materials is tricky, especially when temperature changes and water are involved.

[1] You can use hand calculations to check buckling as well but they depend on analytical models which, if they even exist for CFRP, would be quite difficult to trust because there are so many more variables compared to metals.

[2] Delamination must be really nasty when coupled with buckling. Local weaknesses greatly affect buckling, and a even a small void between plys is a local weakness where the plys don't transmit load to each other.