Hard to get a good read on that shuttlecraft. I think the main disconnect between it and the Valiant for me are the aft engines. Why would the shuttle have a different and seemingly more advanced engine?
design is far more advanced than anything we can likely expect by mid century, but then the DY-100 was far more advanced than what was possible for the 1990s. The point is TOS' universe is not ours and contemporary Trek fell down by trying to shoehorn our reality into Trek's. And so I ignore adhering strictly to what our reality would dictate because it doesn't gel with what Trek and more particularly TOS has already shown us.
The big engine at the back of the Valiant
isn't a rocket engine in the conventional sense. It's one of the early forms of impulse (which possibly came into use around TOS' 2018) but on a big scale in relation to the rest of the ship. In contrast note how small the impulse engines are on TOS era ships and shuttlecraft. The Valiant's
impulse drive (and Kirk in WNMHGB did say the Valiant
had impulse engines) can drive the ship to near the speed of light if needed, but it is a secondary drive. The Enterprise's
impulse can do the same thing, but look how much smaller (in relation to the size of the ship) and faster reacting they are, too.