I understand that it is more flexible to add the effects later, but if I really like the vocal sound with reverb shouldn't I just record it that way? Capturing the moment as we are hearing it seems more authentic somehow.
It may depend on the equipment you're using and how difficult it might be to get that setting back later if you really liked it. On a DAW with plugins your 'risk' is relatively very small.
it's really more about not painting yourself into a corner when you don't have to. A reverb setting might sound great during the recording, but if you're adding other instruments the overall picture may change and suddenly that setting may not work so well, or might be too much or too little. Monitoring the reverb as opposed to recording it will keep the vibe going but still give you the option to tweak before you complete the mix.
If I really like some effects - say someone has some effects boxes on their guitar or something in their amp, I like to get their signature sound (with a mic on the amp), but I also like to have a DI going into another channel at the same time. Then you have both the raw sound to work with and also you've captured the artist's signature sounds. When you mix, you can pick and choose, but you might not get the chance to go back and get the one you wish you had later. You can always mute the one you don't want - or you might want both in some cases.
This could be applied to vocals, too. If you have an outboard effect that sounds great in your session, run that into one channel and the mic directly into another. Then when you mix you can choose according to what you find best at that stage.
In either case, you need something to split the signal from the source to go both into the effects processor and into the direct preamp. I suppose there are cases where you have some great mic pre that impedance matches well with a given mic, and that would preclude splitting the signal before this pre. Then you could split it after the pre. There are numerous ways you could handle this - just make sure your effects don't spill into a mic that is intended as a dry direct input...