20-Year Prospect
There you are in labor, and the contractions are so bad you've already punched your husband and called the nurse every foul name in your vocabulary. The pain's eating at you, turning you into a monster. Time to give up the pipe dream of having a "totally natural" birth and do what more than half of the women in your same situation do: call the anesthesiologist.
These professional pain-relieving guys and gals will definitely be around for the next twenty years. After all, human beings aren't going to suddenly become immortal and find no further use for surgery. That said, there isn't a lot of room for growth in the putting-people-under department.
Why? Well, let's return to the Labor and Delivery ward and do some math. Say you have a ward that delivers 2,500 babies a year, for an average of seven babies a day. It only takes five to ten minutes for an anesthesiologist to administer an epidural to a woman in labor.
In other words, if the seven women on the ward in a given day all have trouble-free epidurals, the anesthesiologist will be with patients for seventy minutes, tops. Do you really need more than one person on the ward at a time doing this limited amount of work? For now, maybe. For the future, maybe not.
So, yes, anesthesiologists will exist in the future. However, given that this is a specialty practiced in hospitals under very specific circumstances (e.g. when people are getting cut open), we don't think there will be a need for many more of them than there already are.