I don't recall anybody ever showing that
Elementary Mode S having any value whatsoever to ATC, or to anybody else, over Mode C.
Hilariously, if you get the installation manual for say the GTX330 you won't find any reference to "elementary" or "enhanced". This is because these terms are a purely European invention, done without looking at equipment actually on the market.
A GTX330 will radiate all data connected up to its RS232 or ARINC inputs.
The better equipped GA could thus radiate additional parameters (certainly GPS position, track, GS, etc) but they are not allowed to because the radiated parameters have to be documented in the POH supplement and such a doc change is an EASA Major Mod, costing 4 digits
So ATC are never going to get the extra stuff which they claim is what makes Mode S useful.
Only some planes, imported with Mode S installed and left on their original registry, emit the extra data.
The image posted by Roffa has been shown by NATS for several years now. I saw it on a visit to West Drayton. NATS have been trying to sell this software to other ATC units and they are very proud of it. But it has zero relevance to GA because GA will never be allowed to emit the data even if it had it.
The other thing is that, from some enquiries made, it appears that the NATS software suppresses the extra data anyway, for "GA" targets. One pilot whose GTX330 definitely emits the GS (because his GTX330 is - like many - set up to use GS to switch between AIR and GND modes) has asked Mode S equipped ATC if they can see it, and they cannot.
It has been a total farce. I recall UK's best known avionics shop publishing a press release a while ago, saying they have to effectively cripple hundreds of Mode S installations, because EASA threatened that radiating the GS parameter is illegal. Later, Garmin promised to modify the GTX330 firmware to include a config option to not radiate this stuff; this is I think in place now but only long after most IFR pilots installed the unit. I have such an installation myself but "fortunately" the GTX330 fails to accept the GS parameter from the KLN94 in the first place so, gosh, I got away with it and I am 100% legal
Roffa may not like this but like I say there is really no, zero, zilch, absolutely nowt, benefit to ATC through GA having Mode S.