I do feel however that an exercise of that caliber should have a place in any program but it's not always a necessary exercise, for me the best exercise is the Bear Crawl; it literally hits your body from every angle and having to move in awkward positions creates a stronger base as oppose to push-ups where you are only going up and down in the majority of variations. Sure the Bear Crawl needs a bit more space but when it happens, you will be huffing and puffing quicker than Peter Griffin's time on a Cardio Bike. I like to make Push-ups interesting or try variations that are a little out there. One way I do my push-ups is using a weighted vest and do them slower with less repetitions with fewer sets to build up testosterone and get more of my arms in the mix. I also use what's called The Power Push-up Plus from Lifeline that makes it more of a Bench Press feel to it where resistance is the main key.
Most of the time I see people doing Push-ups, most of the variations they use are very boring and just so tedious they're not fun. Sometimes too basic becomes dull so spice things up a bit. Going up and down isn't what life is about, it has curves, swirls, circulates and even has you at a dead stop at times. Make your push-ups interesting; do them upside down, do Archer Push-ups, clap for joy and even jump around, have fun with them. If I wanted to just go up and down just do stairs. Be creative.
I've done tons of reps in this exercise well within the hundreds in single workouts so why continue that cycle, sometimes I don't count and bounce around doing a few reps of different variations and goofing off. Doing hundreds of reps a day is boring period, if you're into that more power to you but having a puffy chest can only get you so far. Live it up and do push-ups with a little Flair (and no i'm not talking about Ric Flair's grandkids).