Interesting post, but perhaps the product of your imagination? Seriously, do you really think that they announce "is there a Doctor on-board?" routinely enough to give you this many experiences? It has never occurred in my 30 years of practice.
It's not how long you've been in practice but how often you fly. Data I have from a major British airline indicates that the crew are faced with a medical incident of some kind once every 48 sectors on their long haul operation. I don't have any information about short haul but one might expect fewer problems on short sectors as sick passengers would perhaps be more likely to keep their symptoms to themselves until they are off the plane.
In the last five years I think I've done around 500 sectors (a mix of long and short haul) and I can only remember being asked to help four times.