In partial answer to the question set in the title: it will continue to seem like a dying breed.
There are a few considerations that haven't appeared here yet.
One is the natural limitations on talent. In the 1990's, when the true awfulness of much SW was becoming known to a wider public, a friend of mine, who knew everybody when he started and is still known by everybody, relayed a comment by one of his (even) older colleagues: "you know, when I started in the '60's, there were probably about thirty good programmers in the world. Things haven't changed."
Pick the competence level: there are a certain number of people in the world who interest themselves enough, train enough, and are good enough, to hold a particular flying standard with that level of training and recurrent training. Maybe not all of them are flying professionally, and maybe one can encourage more to do so, but once the level is picked the numbers are thereby limited.
What happens if you need 20-30% more pilots than that? Well, it's going to cost 40-50% more, because the ones you get are going to need more training, more recurrency, more everything to maintain the standard than the ones you already have. Or you're going to have to lower the standard. It's just the way things are.
Now, this consideration isn't decisive. Because we actually do have more talented programmers and computer scientists in the world than we had in the 1990's (let alone the 1960's) and that is because talented people are attracted. Math is dead-end; physics is dead-end; suppose you like technical detail: go into computer security. It's a huge growth industry, starting from almost nothing (pure military apps) in the mid-1980's.
But that doesn't seem to be happening in airline flying because of the Sullenberger-PJ2 considerations. Since I have been reading Aviation Week (mid 1980's) there have been regular letters complaining about a similar situation in aeronautical engineering. Talented people were apparently now going to computer companies or finance (which got technical).
Second is the type of training. The different aspects of understanding and flying the fundamentals versus following the magenta line have been done to death in a few dozen threads here. So I won't reiterate that. But I will say in all likelihood the magenta line wins out. It wins for different reasons than in my first point above; I have in mind two. One is that it embodies judgements about flying logistics that largely cannot be calculated in real-time by two flying crew, so management likes it, even savvy management, and they do run the show. The second is a phenomenon called by John Adams "risk homeostasis" and by some others "risk compensation". I was driven around town in a recent snowstorm by a taxi driver who drove in slippery conditions as if he were on just a wet road. He was relying completely on ESP and ABS to maintain his vehicle in its accustomed mode of proceeding, in case he should misjudge a situation. It worked (not just for my trip, obviously). That's what people do, and pilots and their managers are no different. And it works (until it doesn't). If that is what you are mainly used to, then flying the raw data is going to be proportionately less familiar, no matter what your level of talent and professionalism.
Third is a phenomenon highlighted by Guppy and countered by Jabiman. NA is a place in which you can accumulate the kind of experience recounted by Guppy. So is Oz. For all I know, so is Brazil. Not many other places. You can't get it any more in Europe, and the East, where growth is at present, is not known for its wide-open spaces and inexpensive private aviation culture. So people are going to be ab initio trained and put in the right seat. Like it or not. The question - with 200 hours or with 2000 hours? - has already been answered. I guess that, unless the accident statistics get, quickly, a lot worse, it is not going to go up from where it is now, which is low-hundreds (except in those places with a plethora of high-time pilots without jobs, such as the US). Correspondingly, avionics will be designed to cope with this situation.
There is an article in The Economist this week which addresses some of the economic phenomena of contemporary transport flying. I introduced it, but a moderator thoughtfully relegated it to the "Passengers and SLF" Forum
here, where it is sure to get a lot of attention from those discussing the changes in the flying profession. On a private list, it was discussed by an IFATCA executive, PJ2, and people intimately involved in assessing the major 1990's ATC upgrades in Canada, UK, Australia, and the US. The consensus is that the ATC upgrade problem is not due to controllers' views or actions, but largely due to technical difficulties and the airlines themselves not wanting to move to a variable-pricing slot model. The question arose why avionics are comparatively so advanced and ATC systems up until now so technically troubled (this has begun to change with systems such as iFACTS, which have been developed using Correct-by-Construction techniques).
The reason such considerations are relevant to the cockpit situation is that the beancounters always win (to complete the argument, put this together with my points one and two above). But the question is what beans they count. Do they count the beans they didn't have to grow but might have had to if a couple of truckloads had tipped over on the highway? Not according to PJ2. Safety (which is ultimately what this thread is about) is a hidden variable as things now stand. The trick is to make it explicit, along with its price, and no one here has yet suggested how to do that. To do it, one has to understand the entire economic environment. To my mind, the above article is part of that.
PBL