Delay is sometimes used to create a 'space' as well as reverb. Sometimes a short delay can help to create a space without making the source sound distant like reverb can. Many times something like a combo of a stereo delay sent to a plate verb used subtly can enhance the space without it getting washed out. One trick is to take most of the low end out of the delay before the verb. It can widen stuff without being obnoxious. Just gotta play with it.
I don't have pedals apart from an EQ and do mine in the DAW, if I want to hear it during recording I'll dial in something to play to.
I use Delay more than reverb nowadays. I'll blend in a stereo delay, a slap, and a distorted delay. If I am using a reverb aswel it's normally way quiter in volume. These effects are just brought up enough to be more felt than heard though, if you close your eyes and bypass/enable all those effects you will feel the lead guitar/vocal (whatever is mono and center lead line) get wider and thicker and gel with the rest of the mix, even if you have it sitting on top of the mix it seems to feel much more connected.
Or of course you can use the delay as an effect and turn it so it's almost as loud as the dry signal. A heavily effected signal does sound cool, in a mix i'd much rather have that control though I wouldn't ever be satisfied enough with how the delay stays completely static throughout the entire song and I would feel like it would hurt my production, the delay pedal will mean there is no going back once recorded on the way in.
Edit: Oh and pedal is mono, i'm normally using delays for cool stereo effects, turn that mono recording into something with more interest. So DAW is all I need, Unless i was to play live, I have no interest in a delay pedal. Tone shapers yes.. FX no
Because one day, you might just want a slightly different flavour.
I used delay after a few years and it was very obvious and I liked it then I didn't use it for a number of years. Now, I use it when I want a certain effect. It's like having a toolkit. I rarely need a file, haven't used one since 2008, but on that day I do..........
There are things that you can do with very short delays that you can't do with anything else. Psycho-acoustic stuff. Delays under 20 msec mixed at the same pan point as the source disappear but can make something sound thicker , taller, shorter, up and down. That's just for starters