I, too, would prefer to milk the impressive and lovingly done visuals of TOS for their sweet maximum of lactose content (except perhaps when the visuals are really subpar, as in "Doomsday Machine"). Which means I unconditionally accept the rear spheres and fore spikes as retractable.
The spheres already appear on all the United Earth Starfleet ships seen in ENT, including the modern Enterprise
, the older Intrepid
, and the lifting body ships accompanying the latter in "The Expanse" and "Twilight". They're absent from the conjectural Daedalus
, tho, as well as from the ships of STXI.
In TOS, the spheres are "retracted" in very specific situations - namely, when the ship approaches or orbits a planet, due of course to the nature of the stock footage.
One possible theory: the spheres do things to the putative exhaust of the warp engines, perhaps filtering it for better stealth. A civilian survey ship like Daedalus
doesn't need that stealth, and perhaps the STXI Starfleet also prefers not to block its tailpipes in a manner that might cut on performance. Also, the ships that do have spheres need to open them every now and then for purging - and what better time than just after dropping out of warp but before settling to standard orbit around a planet?
As for the forward spikes, many fan sources have speculated on a "deflector" functionality. Perhaps again something that's useful when entering a star system or approaching a planet and its outer atmospheric layers or magnetosphere, but not generally needed? Or then something related to purging the engines...