It's hard to define 'paddle driven' cars, since of course any automatic transmission car could have paddles that allow manual shifting.

I assume you're talking about the paddle-shifted transmissions found Ferraris, Lamborghinis, BMWs etc. in the recent past. These in fact are the opposite of 'clutchless'. They were basically manual transmissions electronically controlled and with the clutch and shifting actuated by hydraulics.

Nowadays they use some variety of dual-clutch transmission.