The selling point of electric sports cars is more "the acceleration is amazing" and less "it makes a loud noise".
e.g.
> a 0–100 km/h (62 mph) acceleration time of 2.36 seconds, and a quarter mile (402 m) drag race time of 9.78 seconds. ... unofficially the fastest production car in the world
https://en.wikipedia.org/wiki/Yangwang_U9
> Model S Plaid Takes 2.07 Seconds to Accelerate from 0-100 mph
Acceleration is about the only selling point of a sports EV.
They're so ungodly heavy because of the batteries that they handle like barges. They need giant tyres and so much ESC and software control because these things weigh almost 2000kg or more. You can try and work around it but there's only so much that can be done to make 2000kg take a corner.
Looking at where sports cars will be in 10 years with ICEs being regulated out of existence makes me very sad because it seems like we're about to see the death of the lightweight sports car.
I think if you look at e.g. Model 3 Performance it's not quite so hopeless. 80kwh packed into an EV roughly the same size, weight and performance as a contemporary BMW M3. Even with today's technology (0.2kwh/kg, 3-4 miles/kwh) a Miata-sized 250hp, 2500lb, 200 mile EPA EV is possible. Whether that would be a compelling driving experience and anybody would buy such a thing is another question.
The McMurtry Spéirling is under 1000kg. Battery technology will only improve and so I expect to see under-1500kg sport EVs generally available eventually.
Under 1000kg for a reasonable price probably means building your own electrified exocar.
The McMurtry is a race car so it's not surprising it's that light. However it still pays a price compared to its contemporaries (go look at the weights of various LMP1 or LMP2 cars, even old cars like the Mazda 787B was ~850kg iirc). The only number I've found so far is "under 1000kg" so I assume it's probably quite close to that 1000kg number.
The weight of the batteries isn't going anywhere anytime soon. I expect car makers will prioritize range. I think the engineering to make an EV truly light like an old Integra Type R (1100kg) will be obscenely expensive and sacrifice so much on practicality it just won't be a viable product as a road car.
The car would be so compromised to be that light nobody will make the car, at least at an affordable price. You'll end up with a limited range, limited power, uncomfortable car for a price way out of line with what you're getting.
I think you could make a ~150kw-180kw EV pretty light, but considering the ongoing power pissing contest in modern cars I'm not sure how well it would market test.
So I expect the market will stick to heavy cars with big power because it's easier to build and easier to sell.