Good storytelling doesn't need to have artificial limitations because it would be made in such a way to WORK with the established setting instead.
If by "artificial" you mean arbitrary, sure. But if a limitation is plausible and arises organically out of the physics, engineering, or logistics of the situation, then it can be a good thing from a storytelling perspective, because it's good to create obstacles for the characters in the pursuit of their goals. For instance, it's often necessary to prevent the characters from just beaming up out of danger, and there are plausible ways to prevent it that are natural outgrowths of the technology -- for instance, if their communicators are taken so the ship can't lock onto their location, or if there are shields in the way.
To me it would be incredibly dumb for shuttles NOT to have Warp capability.
Technology and science (especially for a spacefaring combination of societies like the Federation) would evolve on an exponential basis.
In mere decades we could downsize supercomputers to something that can fit in your hand and also greatly surpass them in performance and efficiency... it stands to reason in the Federation, it would be more than doable to do that with Warp drive on a shuttle (actually, the Federation should have had much more developed science and technology by those metrics compared to what we saw).
I don't agree. Moore's Law is not a universal; some things can't be as easily miniaturized as others. Warping spacetime is an incredibly difficult thing that requires immense amounts of energy or mass, so it's plausible that you'd need sufficiently large mechanisms and power generation systems to pull it off. Of course,
Star Trek has (once again) always shown that shuttlecraft in the 23rd and 24th century are capable of interstellar travel and therefore must have warp capability, but I've always found it implausible that warp drive could be miniaturized to that degree. In general terms, it's not unreasonable to posit a universe where there's a minimum practical size for an FTL engine, dictated by fundamental physics and engineering limitations. Indeed, there are a number of SF universes where FTL travel requires large, stationary apparatus, like
Babylon 5's jump gates, or massive natural phenomena, like the collapsars (black holes) of Joe Haldeman's
The Forever War. (Or there's my own Hub universe, where the titular Hub, a space warp at the galaxy's center of mass from which all points in the galaxy are instantly accessible, is
the only means of FTL travel ever discovered. That limitation and its consequences are the source of most of the plots in the series.)
At the very least, there's no reason you couldn't set your story at a point in the development of the technology where the means to miniaturize it further hasn't been developed yet, as in the
Enterprise era when shuttlepods were strictly sublight.
It can certainly be narratively useful to make FTL a limited resource for your characters. For instance, a story where the FTL drive is in danger of failure or destruction has higher stakes if the crew has no backup. Or if only really large ships are capable of FTL, you can design a fleet built around a carrier model, where a large FTL-capable ship carries smaller, more multipurpose ships to their destinations. Limitations in fiction are not dumb; they're opportunities to be creative, by showing how your characters adapt to those limitations.