I think the core of this discussion is linked to "essence" of why some cars are considered "drivers cars" vs not. It's the balance of hp, tire, and the ability to not feel like the car is attempting to kill you. Obviously some prefer more or less of the last item, but in general, nobody wants a car that requires 10/10s attention to drive at 6/10s performance.
I'll provide some examples. The e39 M5 is recognized as one of the best drivers cars for a variety of reasons, but I think a core issue is that it is predictable in it's power delivery (flat torque curve with power everywhere), and it has enough HP stock to rip the tires loose whenever you want, if you choose to, but it's controllable and easy to work with, even without any nannies. Obviously there are a lot of chassis/weight balance, and overall "feel" of the car pieces that work in tandem, but the overall package is one that people can feel comfortable turning the nannies off and ripping without scaring themselves.
Similarly, the s2k can get a little sideways on demand, but it's never going to try to kill you, and In general, it could only really do this when pushed a bit. Similarly I think this is one of the reasons why the BRZ was so critically received is that while it's perfectly happy to be pushed to the limits and on the stock tires you can have a bit of predictable fun at the limit, as soon as you add more tire, it's boring and doesn't have enough power to do anything.
I think the v2 fits this in general, although I think many would argue that in stock form maybe it loses a little bit of fun factor to an e39 m5 because of the higher power making no nanny mode a rarer driving experience, but it makes up for it with the "comp mode" where you still have some protection from truly fucking up. I would say this is where tire is more critical, and what the OP said about feeling like they're on iceskates, that's 100% because you're on the wrong tire for the weather. I can do a full 2nd gear pull in my stock wagon with my winter tires, and unless it's wet, I get full traction. Summer tires are not usable below about 50*F
I personally think that turbo cars add a fun factor in the "ramp rate" of power delivery, which is unpredictable and provides a bit of excitement, but most of my higher HP turbo cars have all been AWD, and with that, it balances the unpredictable nature of power delivery out with a natural ability to compensate for it.
And this is where I think the future will go, more and more electronic nanny settings that let you have some fun, but with a safety net. I think the days of "push once for everything off" are definitely gone.