if i steadily worked my way up to say 100/150 consecutive push-ups a day — is that enough of a workout? do i really need something else? right now I can do 10

Yes, and you can do them in whatever # sets work for you. A great minimalist daily workout is 100 squats, 50 push ups, 50 pull ups. Over time you can push yourself to get all your reps done faster, or increase total reps, or increase difficulty (e.g. weight vest)

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Also if you are struggling to do 50 regular push ups, try to get your rep count done using easier variations e.g. push ups on your knees instead of on your toes. Then as you get stronger you can do more of your reps on your toes, then progress to harder variations.