I thought computer recording was too complicated back in the days when you had to buy a special PCI card, maybe an ADAT machine, mixing board of some type. It was complicated, and expensive. I bought my first digital recorder in 2003, a Yamaha AW16G. I liked it, it wasn't terribly complicated, and the sound was nice and clear.
Today, I've got both worlds, a self contained digital recorder, and a DAW/Interface setup. I can record on the first and mix later on the second (great for portability), or I can just plug mics into the interface and go straight to the computer. I'm a Reaper user for a few reasons. ProTools might be nice but there's no way I'll pay the annual license fees just to play around in the basement a few days a week. I have 3 versions of Cubase LE, and it worked fine, but I tried Reaper and really liked it. I'm on PC, so Logic/Garageband are not available.
As with any system, once you learn the basics, you can be up and running in about 3 or 4 minutes. Boot the computer, pull out the mics and plug them in, fire up the DAW and load up a template of tracks that you've already set up. Hit record and away you go. You don't have to do everything piecemeal, cutting and pasting snippets to construct your song. You can play the whole song in one take, go to the next track and add all the vocals, or add all the harmonies. Punch in a solo if you want. Work it just like you did tape. Just because you CAN cut and paste with a couple of mouse clicks doesn't mean that you have to do it that way. You have the choice of how you want to operate. Use what you're comfortable with.