You have a few correct points but are mostly spreading misinformation. Repeated exercise will only improve efficiency by a few percent at most, and then only for certain activities. For cycling, efficiency hardly improves at all. The calories shown on gym equipment are often nonsense but the latest generation of fitness trackers are reasonably accurate and can be worn 24/7.

You have to get into really long cardio sessions with no carbohydrate supplements before that has any significant catabolic effect. This is not a concern for casual athletes.

Strength training is great, but it should be combined with some form of cardio in a comprehensive fitness program.