It's a fair question. My car before this was a twin-turbo V8 with a great sound. I missed it for a short period when I moved to the P90D, but that didn't last long. If anything, I appreciate that the car does not sound obnoxious if I feel like taking off from a light, and that it is not too loud in the mornings when driving on smaller streets.
As for the connection with the car, I wondered about that also but if anything I feel more connected with this car. There are several reasons for this - the handling is great, as I mentioned above, and it has pretty solid road feedback. Interestingly, though, the acceleration pedal gives you a very well defined response to any given level of pressure. There is no "lag" of any sort. Even with a large ICE without turbos, you never really have immediate response to the throttle. The car basically does exactly what you want it to do exactly when you want to do it, so it feels that much more precise. I cannot imagine what this feel would be like in a smaller form factor (e.g. Roadster 2.0) but I would love to find out.
The car really feels nothing lie a golf cart, any more than any other gasoline-powered sports sedan would feel like a gas-powered lawnmower. The comparison is not valid. It also is VERY different in feel from a Chevy Volt or Nissan Leaf.
All I can say is that if you are at all skeptical, take one for a test drive. I was too, until I walked into a service center a few months ago and took a P85D out. At this point, I cannot imagine ever wanting to go back to a gasoline car.