I think the idea that impulse is a FTL technology is highly dubious. It does have to involve relativistic effects and require some sort of compensation for them, because the speeds approach FTL (remember the Warp .5 comment from Kirk in TMP? That was on impulse was it not?) That's about as close as you can call impulse to warp.
The Final Frontier shuttle was different from previous shuttles because it was a redressed shuttle from TMP. It was a budgetary issue which made it more anachronistic, although you could argue that at that time-period, more TNG-like tech was bleeding into Starfleet (like the Okudagrams that really got their start at the end of Trek IV which was before TNG even debuted). Most Trek fans, when asked about shuttles back in the day, would tell you they were not warp capable, or if they were, it was very limited and impractical compared to starships, and might not have been standard equipment.
The whole idea of a shuttle was to provide a backup for transporters to ferry people and things to and from planets and starbases. They were never meant for anything more than that and it was only later on in the TNG era that they started adding more amenities to shuttles (like the DS9 runabout) so that they could act more like long-range RVs.
The story idea behind a shuttle was to provide a more fragile means of transport to heighten the drama, as we saw in the Galileo 7 episode. This way, if for whatever reason the crew had to be left stranded on a planet, even with a fully functional shuttle, they would not be able to make it back to civilization. It was a glorified rowboat.
The problem with TNG in general is that the technology became so much better and more infallible that the risk of space travel was almost completely lost. Shuttles not only got warp, but weapons systems, shields, mini transporters, and even bunks. They just became miniature starships, and it just was the wrong direction to go.