You are right F-15 are Energy fighters, but F-16 are also Energy fighters… so this does not explain why the first should not be flown like the latter.
F-16 is optimized for high sustained turn rate in high subsonic (M0.7/0.9) and is also a very good climber, when F-15 is optimized to be the best climber and for high (compared to other planes) sustained turn rate from high subsonic to low supersonic.
So, Eagle will be better than any others (even better than a F-16) in these 2 areas : pure climbing and sustained supersonic turns…, so let use it where it is the best.