Here's the issue: errors with a single blade safety razor are much worse. I didn't cut myself 99% of the time, but when I did, the cuts were large divots out of my skin. It sucks.
Go with the modern technology and leave the single blades to the obsessive.
Keep in mind I haven't done any stop-watch studies...
Shaving with a normal razor takes me about 5-7 minutes (I still use a plastic 2-blade razor when I travel). The DE razor probably doubles that, maybe in the range of 10-12 minutes.
At first it was much longer, like 15+ minutes until I got the feel of it. But after developing a technique, it goes pretty quick overall. Either way, the additional time is still on the order of 10-15 minutes at most, and should be an extra 5-8 or so when you get the hang of it.
As for time and enjoyment, it takes me probably 15+ minutes because I'm still getting the hang of it, maybe even 20 if I'm practicing a 3rd pass (for the perfect shave, you go with the grain, across the grain, against the grain, and your face will be smooth in all directions), but I feel good when I'm done.
My favorite one regularly goes for about 5 bucks (They are usually tagged with: Canadian 1932 "military issue" like these: http://cgi.ebay.ca/LOT-2-GILLETTE-SAFETY-RAZORS-3-PIECES-BLA...).
The first week I shaved before bed to get the hang of it. Went slow, paid attention to technique, beard growth direction, etc.
After that I shave almost every morning after my shower. Takes ~10 minutes including Lather, Shave and Cleanup.
For me, I like it. I have a small collection of some cooler looking old DE razors. Buy blades for incredibly cheap. And can enjoy a variety of shaving creams.
Depending on things it would take me between 20-25 minutes to shave (using a Merkur, forget which one it was exactly) but I wasn't good at it at all, so you could properly cut it down to 15-20 minutes.
And there is nothing as good as getting out of bed at 5:30 to start a productive day.
I also only shave every other day, in large part due to how close of a shave you can get, though I also naturally don't grow hair quickly.