We use every imaginable angle with push ups, and utilizing the handles helps ease strain on the wrists while allowing for more experimentation.

the elbows will flare out with a thumbs in grip but you will still be hammering away at the triceps.

i still prefer to work the triceps through various push ups than to use a pushdown / pulley machine.

Especially when training athletes, the push up is highly economical and gets a lot of work done.

For our HEAVY guys w/poor GPP, we have them perform push ups for moderate reps in between sets on lower body day and high reps at home on "off" days.

This has boosted GPP and bench press numbers, both of which raise their confidence and in turn improve performance.