Navies frequently put out, um, 'optimistic' numbers on ship speeds. A number of French and Italian ships were supposedly able to attain 36-39 knots at sea trials before WW2; left unsaid was that no guns or ammo were aboard, and that the final loaded ship speed was as much as 6 knots less. The US also put out that its nuclear submarines were capable of as much as 42 knots when in reality they could make a bit over 30; silence is much more valuable to a sub than speed.
Nuclear carriers can steam at high speeds for long periods of time. They no longer have to use high speed to launch aircraft (though the breeze over the flight deck doesn't hurt) and instead need strategic speed - the ability to run from California to Japan, or Virginia to the Middle East, in a short period of time.
Last information I saw was that the later generations of nuclear carriers had thicker lines (to carry more stuff like bombs and fuel) and therefore could run in the 30-32 knot range. There just isn't any tactical need for higher speed, and tonnage not spent on engines can be used for jet fuel, bombs and planes.
With any steam-driven ship you can exceed the suggested limits and work the engines harder, at the risk of catastrophic failure (steam lines go boom; turbines shed blades) or serious wear-and-tear, and for little gain. Because of the rules of hydrodynamics, a ship can usually reach 75% of its rated speed at half-power (that's a very loose approximation and should be taken with a bag of salt, but it will do). It is the last little bit of speed that needs huge amounts of extra power. Battlecruisers were able to steam like a cruiser (their intended prey) but at a high cost in tonnage:
Ship type Ship name Tonnage Engine SHP Speed Armament Armor Belt
Battleship Iron Duke 30,380 29,000 21 kts 10x13.5" 12"
Battlecruiser Lion 29,680 70,000 27 kts 8x13.5" 6"
Battleship Koenig 28,200 31,000 21 kts 10x12" 12"
Battlecruiser Seydlitz 25,200 67,000 26 kts 10x11" 10"
Cruiser Arethusa 3520 40,000 28.5 kts 3x 6", 4x4" 3"
Destroyer Paragon 900 22,500 29.5 3x4" -
Fast Battleship Hood 47,500 144,000 31 kts 8x15" 12"
'Destroyer' Le Fantasque 3400 81,000 45 kts 5x5.4" -
These ships are all rough contemporaries, built around 1909-1912 (Arethusa and Paragon from 1912-13, Hood from 1920 and Le Fantasque from 1933). This not only shows some differences in British and German theories as to what a capital ship should be, it shows the immense extra power needed to achieve a small amount of extra speed. (Not shown is the superior German subdivision scheme or the British practice of piling propellant and shells in the turrets). The German engineering plant used 3 props instead of 4; the middle shaft was pretty much wasted and usable only as a spare or for full power. Note the extreme high speed of Le Fantasque - three times the tonnage of contemporary destroyers, and the huge size and power of Hood.
Now admittedly, space maneuvering must be different from steaming over water. It may well be that a hyperdrive (or whatever we use as thrusters) works better for bigger ships than small ones - I have no way of predicting any of that. But on the water, very few navies built small slow ships - big ships needed guns and armor, small ships needed maneuverability and speed, and above all ships were built to work at specific jobs. Cruisers and destroyers defended against subs (and aircraft), or made high-speed runs to get in close and attack with torpedos. And ships of a given generation all had the same range of speeds so they could efficiently work together.
35 mph is about 31.5 - 32 knots (a knot is 1.1 mph roughly).
Sorry for the lecture - naval history is a long-time passion.
