Yes and no. “Strong” is even more vague than “need”. Competitive powerlifters can be gauged as “strong or not strong” based on the squat and deadlift. With anyone else, you’re comparing them with a measuring stick you’ve personally decided on. I can say if someone doesn’t power clean, they’re not strong. It’s an equally arbitrary line in the sand.
For example, was Dorian Yates not strong barbell rowing 405 for reps, stiff-legging 375 for reps, and hack squatting 400+ for reps, because he didn’t “squat and deadlift”?
To be fair, I’m assuming your initial statement referred to back squats and conventional deadlifts. If I’m wrong on that, the situation changes, obviously. I would agree that some squat variation and deadlift variation should be part of the plan, especially for beginners.