ED can certainly be indicative of other health problems but it's just one of many possible indicators.
There are many, including doctors that do believe this to some extent. There was a link that was first made known, for example, in 2002 that heart disease and weak erections were noticed. And years later, they found that erectile dysfunction was predictive of future heart disease. I think any man, especially a younger man, with weaker erections should talk to your doctor about it and perhaps begin monitoring. Also, as we all know stress can impact this so would try to also monitor that to see if it is impactful. https://www.webmd.com/erectile-dysfunction/features/erections-happy-healthy-hard
Not sure why one would think about this, but no. While the ability to get an erection consistently is a sign that part of the body is working well and also indicates at least a small measure of mental health as well, the body has a lot of parts and getting an erection doesn't mean they are all working. In fact, what some men do in order to get a constant erection can be quite harmful. As a man ages, stuff happens. But while that may affect the consistency of the erection, it may not reflect more important body organs one needs to be healthy in order to keep living. So I guess it all depends on what you mean by healthy, as not everyone defines this the same way. For some, it's how long you live. For others, it's how much you enjoy life while you're alive quite apart from how long that might be. For others, it's not how long you live but how good you feel and how much you can do, which is different from merely being able to keep breathing. So in sum, being able to get an erection does indicate the part of your physiology and mental state that controls that is working and that's a good thing. But you could be slowly dying from liver disease while this is going on, if you get my drift. An interesting side note is that there are philosophies that have existed throughout civilizations that abstaining from sex is the key to health. Chew on that one for awhile.