Uh, sources for that? As I powerlifter I have lifted with world class lifter who have a huge variations in their exercises. Bands,chains, boxes, pause/no pause, grip width, stance width.
The reason that works for a world class athelete is because they're extremely careful and persistent to periodize and have progressive overload.
Unless the commenter is an equivalent exception, it's bad advice to follow that, or any other, kind of advice from exceptional genetic folks.
It's very difficult to select the correct weight for an exercise when you're constantly changing it up.
What you're describing are simple modifications as a form of progression. Adding a band to a barbell bench press is still a barbell bench press. But going from barbell bench press, to weighted push up, to (incline|decline|flat) dumbbell bench, to iso lateral hammer machine, to smith, to (low, mid high) (cable, bench) flyes, to dips, to ... Is detrimental.
Most folks should try 12 weeks of the exact same exercise per body part with a RIR3, RIR2, RIR1, RIR0 cycle. (increasing weight each week and from cycle to cycle) . And most folks can do a reasonable selection of exercises for a year or two before they need to tweak for imbalance or personal details like insertions, or weaknesses.
Variety has also helped me do weightlifting without injuring myself. I hurt my back pretty badly doing back squats, probably because I was leaning forward too far, probably because I was overcompensating due to quad dominance. Because of an app like this website I was able to discover and try different squat variants that are helping me fill out the core and glute muscles I was lacking. Again, seems like a good thing.
But it's detrimental to a progressive/scienctific-like approach to lifting.
We want to know that over time we're getting progressive overload. That means you need consistency to watch that 1) The weight goes up for the same reps, or 2) the reps go up for the same weight (or 3, both). Unfortunately exercises are not direct replacements for each other meaning you cannot simply do the same for a variety of (eg:) bicep curls.
Once someone gets past what linear progression can achieve (see Strong lifts 5x5 app for example) then we start to do periodization or other plateau breaking patterns.