...Would an immobile base really care for a versatile vehicle that can do spaceflight, atmospheric flight and surface and subsurface travel in water? Rather than accept the compromises, the base would probably want a thoroughbred submarine...
If TAS had never introduced the aquashuttle I'd agree with you. But TAS did introduce it so now I'm just trying to reconcile it in a more credible form (as I see it anyway). This version doesn't have warp drive and I jettisoned the nacelles because I don't feel they fit for a vehicle supposedly made for underwater operation. My version is a strictly orbit-to-surface (and return) craft. It doesn't even have impulse but is propelled (for atmospheric and limited spaceflight) by an antigrav system.
I've scaled it down from what was seen on TAS but nonetheless it still remains a sizeable craft and one which I think unlikely to be kept berthed as part of a starship's regular shuttlecraft complement. So my thought was it could be a specialized vehicle loaned out temporarily to a starship for specific missions (same with the lander version I did previously).
In a more credible scenario such a craft might not even belong to Starfleet, but rather it could be owned and operated by a separate science and research agency within the Federation and essentially given a ride to its destination by a Starfleet vessel, assuming the destination lies outside a given range normally reachable by non Starfleet ships.
In the past and even today naval forces have worked with civilian agencies. Governments aren't the only ones who conduct scientific research and onsite study.