Well, humans were dreaming of building warp 7 ships as of "TATV". One wonders if anything ever came out of it.
Is Kirk's ship a warp 7 vessel, say? Scotty gets a cardiac arrest every time Kirk orders a speed higher than warp 6... OTOH, it seems that any ship can reach arbitrarily high speeds with sufficiently many people sitting on the safety valve - this merely shortens the expected lifetime of the ship and the crew to varying degrees.
Archer's ship for some reason never had to suffer the indignity of traveling way faster than the recommended maximum speed. I wonder why? Something inherent in the engines? Or just a general strategy of avoiding tugging Superman's cape?