THE ANSWER: It depends...
Lifting to failure is 100% not necessary for gains and progress. If done too often, it can be counter productive if strength and muscle hypertrophy is the goal.
For Compound lifts (like Bench Press, Squats, Deadlifts), going to failure can even be dangerous in the sense of you getting hurt. Going to failure is more safe during single joint or isolation movements. I.e: Hamstring Curls, Leg Extensions, Machine work, Lateral Raises, Arms, Calfs etc. Those are low risk movements and going to failure CAN be helpful to tax smaller muscle groups.
Going to failure and pushing it to max. Can be useful for muscle hypertrophy by creating metabolic stress. Just remember to get a real good warm up, and use this less frequent (so once in a while, preferable at your lasts sets) If you are feeling joints & muscles are achy and recovery takes longer, then listen to your body first!
Take the time needed to recover between training sessions and get quality sleep. If you have been training heavy and hard for a couple of weeks and feel like your burning out. Do a deload phase of one to two week with lighter weights or more time off the gym.
I love using RPE (Rate of Percieved Exertion) for strength training to get the most out of your training sessions and working sets. Use my chart (below).
Lifelong gains are made by MAXIMISING Reward and MINIMIZING Risk. It's a marathon not a sprint! So leave your ego at the front entrance and focus more on keeping all your sets with perfect form and the muscles challenged with weights your can control. Learn how to optimise your training, instead of spending countless of hours wasting your time with minimal results and danger of injury by improper lifting technique. Listen to your body's signals, push yourself to the max at the right time, but don't burn yourself out every session!