Most people who ask about meal replacement shakes aren't choosing between a shake and a sit-down breakfast. They're choosing between a shake and skipping breakfast entirely, because they're already running late. That's a different question, and it deserves a straight answer.
The honest comparison
A cooked breakfast you actually sit down and eat is a good breakfast. Nobody is arguing otherwise. But if that's not happening on a Tuesday at 6:45 in the morning, comparing a shake to it isn't useful — you're comparing it to a meal you weren't going to eat.
Against skipping breakfast, a shake is simply something rather than nothing, and it takes about as long as getting into your car.
Why "quick" matters more than people admit
The best breakfast plan is the one that survives a bad morning. Plans that need fifteen minutes and a clean pan tend not to. Something you can pick up on the way, already made, tends to.
That's the whole case for a shake, and it's a practical one rather than a nutritional one. Consistency beats optimisation when the alternative is nothing.
When a shake isn't the right call
If you've got time to cook and you enjoy it, cook. If you have specific dietary needs or you're managing a health condition, talk to your doctor about what your mornings should look like — that's a conversation for a professional who knows your history, not for a shop counter.
A shake is a convenience tool. It's good at being convenient.