It is all well and good to say "follow your heart" or "do what you love"; but if you want to get an NROTC scholarship and a sure path to a commission, it is important to understand that the selection board cares much more about its own needs - to fill its quota of tech majors - than your personal desires. It is possible to get a Tier 3 NROTC scholarship, but it isn't very likely even for the most qualified candidates; and if you get one, you will still need to take a year of Calculus and a year of Physics.
The horror stories about failing out of engineering are misleading. Any student who is competitive for an NROTC scholarship has the ability to successfully complete an engineering degree - but they will almost certainly have to work harder and manage their time better than students who are majoring in history or political science. Most students "fail" engineering because they don't want to put in the work, and their egos are too fragile to accept the fact that they will routinely get B's and C's instead of A's. The Navy has made it quite clear in its scholarship selection criteria that it strongly favors candidates who are willing to take the more demanding path.
As to the choice between majoring in Engineering on the one hand, and Math or Physics on the other hand, there is no question that Engineering is the most practical choice - and certainly the one that will open the most doors for you, in or out of the Navy. It is well worth the extra effort.
Whether or not you ever commission as an officer, anyone who graduates from college and is employed by any sort of organization soon learns that work is different from school, and that you have to perform all sorts of tasks on a day-to-day basis that are difficult, unfamiliar, and not "what you love". But mature people understand that there is a bigger picture, and that we must accept sacrifices and compromises in order to accomplish our larger goals. In my opinion, it is to the advantage of NROTC scholarship candidates to adopt that perspective now, and to choose to pursue a technical major.