If the point is to burn calories, then shaving weight off your equipment is counterproductive.

But if it makes you want to ride more, then great!

Well, not if you still want to have some fun while doing so.

But I agree, that a regular bike should suffice and you don't need to worry about optimizing gear weight if you're not competing for anything and just ride it for your own well-being.

Well, not necessarily. A bike that's got a full carbon frame also absorbs shock and vibration from the road better. This means you can ride longer distances without getting fatigued in places like your wrists or ass. Longer rides = more exercise.

But once you have a carbon frame, chasing grams on other components gets to be a bit silly.

There's a bell curve. If you burn out too quick you're not gonna get nearly as much cardio, and the torque required to move a real clunker is extra stress on your joints. Plus it's just not as much fun, cycling is a sustainable exercise largely because it's fun. But it's very true that a decent workout bike can be had for $100 if you look. My two workout bikes were both built in the 90s.

That's a stationary bike

And then you have E bike companies producing lead bricks that are non-functional without the motor doing 90% of the work. Or with the massive motorcycle seats that make pedaling actually impossible.