I have been told that the service academies and ROTC love to see that someone is applying to multiple academies and ROTC
I can't speak for the other SAs, but USNA doesn't care whether or not you apply to more than one SA and I'm not sure they even ask. They are interested in whether someone is also applying to ROTC, but I've seen no evidence to suggest that doing so provides any benefit in your application to USNA.
I suggest that candidates apply to those SAs and ROTC programs that they actually want to attend/participate in, NOT just because it might "look good." Some people are just not interested in attending ROTC (or a SA) and thus shouldn't feel the need to apply to both programs. Just be prepared to explain why you don't want to do ROTC, if asked (less likely to be asked why not doing a SA).
The same goes for SAs. There is no reason to apply to any SA if you don't have a desire to attend that SA. You won't get "bonus points" for doing so and it's a waste of your time in completing the application. I realize that kids may not be certain which SA is right for them and views may change especially after a visit. That said, most have some inkling that one or more of the SAs is not a good fit and in almost all cases, that view isn't going to change in the next few months.
The above said,
MOCs like to see candidates apply to more than one SA for two reasons. First, some of them may believe that it indicates a greater desire to serve (personally, I'm not sure that's true -- being focused about your military future is also a good thing IMHO). Second, and selfishly for them, if you apply to multiple SAs (other than USCGA), it gives them more flexibility in giving you a nom to at least one. And they're about making their constituents happy. The danger in this, of course, is you get a nom to your 2nd, 3rd, or even 4th choice and no nom to your first choice. But that discussion is for another day . . .