Resistance training performed to momentary muscular failure, with maximal concentric velocity and a controlled eccentric phase, induces skeletal muscle hypertrophy in humans.

Study: Investigating the Effect of the Tonal Drop Set Mode On Elbow Flexor Hypertrophy

Both workout styles made people’s biceps bigger, so doing heavy lifts until you can’t do another rep does cause muscle growth, even if one way is faster.

Study: Similar muscle hypertrophy following eight weeks of resistance training to momentary muscular failure or with repetitions-in-reserve in resistance-trained individuals

Lifting weights until you can't do another rep does make your muscles bigger, but so does stopping just before you can't — both work about the same. You don't have to go all the way to failure to grow muscle.

Study: Resistance training beyond momentary failure: the effects of past-failure partials on muscle hypertrophy in the gastrocnemius

This study found that lifting weights until you can't do another rep makes your muscles bigger — and doing a few extra tiny reps after that makes them grow even more. So yes, pushing to failure helps muscles grow.

Study: Effects of drop set resistance training on acute stress indicators and long-term muscle hypertrophy and strength.

This study found that lifting weights until you can't do another rep (even with fewer sets) made muscles grow bigger, which supports the idea that pushing to failure helps build muscle.