I haven't owned a c6 but I did own a c5z with a pretty radical LS7 so kind of a hybrid c5/c6.
In some regards the car was very entertaining as a street car, you can idle along in almost any gear and still have ample power to pass without requiring a downshift. When you weren't flogging it the car would regularly return high 20 low 30mpg. The AC was some of the coldest in any car I've ever owned which I loved in the summer and overall it's quiet/supple enough to not bother you as a daily. Rev matching downshifts on the rare occasion you needed them was enjoyable and so was sitting at stop lights both things let you hear rumbly v8 noises (if you're into that, I totally am)
The things that made the car not so ideal of a daily driver were the same things that made it so much fun on the track/autox. The massive 315/335 sticky tires caused the car to hunt and tramline around on the highway/backroads and my track oriented alignment made it twitchy. It was ok to drive to work on a sunny Friday when you're wide awake and ready for the weekend but it was a bit unnerving at times when you were just a touch less focused (like on your way home Friday after a long day at work)
Those same tires also took any joy out of twisty roads on the street. As Seth said, you're playing at a different level than anyone else, even ignoring those suggested speed limit signs and instead going the posted speed limit you could negotiate any corner you encounter with 1 hand on the wheel and a coffee in the other. Heck, you can darn near take 90 degree right handers onto a different road at the posted 55mph without drama. So fun driving roads really became nothing more than scenic routes, Conversely my TDI takes lots of work to come anywhere close to maintaining the speed limit on those roads and is kind of fun.
Lastly the power. OOOOO this was by far my favorite and most useless part of the car. I've never before or since owned anything with that raw glue your head to the headrest thrust in any gear at any RPM of the vette. It was intoxicating, it was fun, but even if you tickled it for just a moment you would be doing triple digits, The reality of the car is a WOT pull in 1st gear to redline is all it takes to exceed every speed limit in Ohio, everyone familiar with a manual transmission knows 2nd/3rd gear is where a lot of the fun is, but you never get to play there because you've already broken the speed limit in 1st.
All of that aside I still want a stock worn beater c5 as a daily driver because I think you could argue it's a perfect MI daily driver, the aluminum suspension/fiberglass body won't rust in the salt. It returns acceptable fuel economy, it's similar to maintaining a chevy truck, parts are cheap and available, and if you jack the suspension up to it's highest setting it has plenty of ground clearance for winter except for those 2 snow storms we get each year.
I think you have to drive one and decide for yourself, they do lots of things well and the power is fun, daily driving something faster than most other people certainly makes long commutes less stressful than the TDI where I have to actively plan my pass for miles.