Ok guys, i've been thinking about this, and how controversial it is. So here's my verdict. Abarth, we all know they are just Fiats with T-jet engines (and good engines they are too) I think it's nice Fiat decided to revive the brand after such a long dormant spell. It's linked to the old race/tuning name, but that doesn't mean they're just going to build a race prepped shell for the track (even though technically they have what with the Assetto Corse, and the R3T priced at around £50,000 a piece!)
We can see that Fiat like to recycle their cars (Panda/500/punto engine/Ford Ka etc) which helps keep design/production costs low and efficient. So as there is already a 500C, why the hell not have an Abarth 500C? We can see they have built a Panda, Panda 4x4 and as a result, maybe a 500 4x4 which has no link to the past at all, and really has no relation to anything produced by Fiat for decades.
Not many people today (especially young 'uns) make the link between the brand Abarth and the old racing days when Abarth were in their prime, so having a convertible version of a fairly quick stylish car is imo a good thing and can only appeal to a wider audience. I think whilst the Abarth 500 appeals to both young, old, male, female, the A500C would appeal to mostly girls who perhaps want all the style and thrills of the A500, just with that added girly side, and maybe those who are considering a 500C who would be willing to stretch their budget to get a slightly quicker car with more extras. I will quote myself again
"the A500C is not making the A500 worse, it's making the 500C better"
Remember folks, the majority of people buy cars these days for "image" the 500 is as others have said a lifestyle car with an appealing image. I'm guessing 90% of people who buy an A500 will never race it or track it, and i'm guessing that almost 100% of those who buy an A500C will never do this either.
So that's my verdict, like it or lump it. I think my mind was clearer before i started typing this (probably my fault for watching the Butterfly effect just now!)