Tartar would easily fit on a Daring. An October 1956 idea was to fit Tartar in X position and two Mk 74 directors replacing the torpedo tubes with a new 35ft lattice mast around the after funnel.
Yet by 1960 when the RAN asked the DNC to look into a Tartar Daring and County the design studies showed no worthwhile missile battery would fit on Daring and it really needed a 4,000 ton hull for a viable ship. The County went up to 5,200-5,800 tons but was rather overloaded (Tartar with 2-channels of fire, 2x 4.5in Mk.6 (one might be replaced by Ikara), two Sea Cat, 2-3x Wessex and steam powerplant).
A new missile Daring came out at 3,900 tons with 26.5kts speed (1 or 2 4.5in Mk.6, Tartar with 42x missiles, two quadruple Sea Cat, Ikara and space to land a Wessex, Y.100 frigate powerplant).
Another Daring-derived design had Tartar and Ikara forward with one 4.5in Mk.6 mount aft.
The next had Tartar, Ikara (14 missiles) and an 80ft landing deck for 2-3x Wessex on 5,300 tons which then ballooned further to 6,300 tons!
County based designs, simply replacing Sea Slug with Tartar aft and steam powerplant came out at 5,783-6,431 tons.
Tartar's electrical power was 350kW compared to 370kW for Sea Slug so generator savings could be made in the County.
In the end the DNC abandoned work as it was eating into RN design capacity and the RAN wasn't happy and the Charles F. Adams was much lighter. I think probably the RAN's insistence on steam powerplants (which were heavier than US sets in general) and fitting Wessex were the driving factors in inflating hull size and weight.
In 1958 when the Leander Class design was underway it was decided not to waste money on modifying Type 12 for Tartar given the small margins for future upgrade later (tonnage wise). It was found Tartar and is required SPG-51 and SPS-26 or SPS-39 would require a 370ft hull of 3,060 tons with a maximum speed of 27.25kts or 27.5kts on 3,000 tons by reducing the bunkerage (range fell to 4,200nm). The radiation hazard from the radars meant enclosed guns were needed and Tartar was expensive. Fitting Tartar and Wessex was again too much for the hull without reducing range or speed.
With Tartar ruled out by 1960 the planned Daring modernisations stuck with 4.5in guns and added Sea Cat, Wasp and a Type 199 VDS.
SIGS was meant to be capable of replacing a 4.5in mount and it was assumed a smaller 26x missile system would replace a 4.5in like-for-like but when India asked for a SIGS Leander variant it was found it wouldn't fit. The CF.299 Frigate designs that led to Type 82 had their origins in designs that used Leander's machinery set but were larger and heavier, 3,500 tons deep.
I think it may have made sense to refit the Darings with Tartar, their proposed refits were cancelled because their £3.5 million cost equalled a new-build Leander and the refit offered nothing a Leander couldn't do except for an extra 4.5in mount and extra speed. A Tartar might have tipped the balance in favour, but of course the refit costs might have been even higher and of course it still doesn't solve the problem that the hulls were approaching 20 years and had little effective time left to make the refit value for money.
Refitting the Counties makes less sense, purely due to the investment already sunk into Sea Slug and its greater range, but perhaps the latter four ships could have been redesigned to optimise the hull design around the more compact US missile system, but that would have cost more and used up design resources and delayed delivery.
It might have made sense to go ahead and create a larger Type 12 with Tartar (an alternative Leander) but the result might have been more expensive and larger and possibly shorter-ranged and we probably would have lost the Ikara and Exocet conversions later on (unless Wasp was sacrificed for Ikara aft). However its Type 82 successor with Tartar/Terrier might have been available sooner and been a slightly smaller vessel and quite successful. SIGS though probably would have been killed off but that would free R&D resources for other GW projects.