Waivers for asthma are not as difficult to receive as people make them out to be. Each case is reviewed both by DoDMERB and if DoDMERB does disqualify, then by the waiver authorities. No two applicants are alike in their admissions package, the same way no two applicants who have asthma are going to have the exact same symptoms.
If you are interested in a service academy or ROTC program I would go ahead and apply.