Is it worth it to exercise to the point of muscle failure

Recovery is an important part of the training process. Stresses provide a stimulus for growth, but hypertrophy itself occurs during the rest period. Therefore, in order for muscles to grow, it is important to give your body enough time to recover, otherwise at least part of your efforts will be wasted. Training to failure slows recovery by 24-48 hours.

This means that push ups won’t work for you if you train a muscle group every other day: they simply won’t have time to recover.