In general there is no proven value to periodic physicals for healthy patients who aren't managing some sort of medical condition. This has been extensively studied and periodic physicals don't seem to produce better outcomes.
https://www.ncbi.nlm.nih.gov/books/NBK82767/
There are a limited set of periodic screening tests which are recommended for everyone based on actual scientific evidence. But those are different from physicals.
Speaking as a family doc, evidence-based medicine geek, and diver over 65,
@Nick_Radov is absolutely correct (and, alas,
@kinoons about lack of evidence for most cancer screening tests improving all-cause mortality, though that doesn't mean they're useless - e.g., preventing younger women from dying from cervical cancer is worthwhile even if it doesn't significantly lower their all-cause mortality). In the "annual physical," the value comes primarily from time to catch up on things like overdue immunizations and recommended screenings (hence why the Medicare Annual Wellness Visit covers those and not a "physical") that often don't get done in problem-focused visits. Cardiac stress tests in asymptomatic people have similarly been shown to be of no benefit. Does that mean that, if you're an older, out-of-shape smoker that you should just "dive in"? No - you should
gradually work up to the level of exertion your diving would require; if you get any symptoms, then get evaluated. If getting basic OW cert., if you have issues in the pool sessions, get evaluated before you do an open water dive.
Is there increased risk of cardiac arrest with diving, as with other exertion? Sure - and cardiac arrest underwater is pretty unforgiving. But doing things that have been shown not to improve outcomes is unlikely to help. On the other hand, do NOT ignore symptoms that could suggest a problem. And if you have a history of heart disease, etc., then you should get evaluated by someone knowledgeable about both your condition(s) and diving. In the case of an older male with a long smoking history, I would suggest consulting with diving medicine doc as there may be evidence about risk evaluation for smoking-related conditions that most docs (myself included) wouldn't know. And Medicare may not cover that.