How popular can Pathfinder possibly become? Could it actually surpass 4E  as the most popular (most played) RPG on the market? And more so, does  it even 
want to?
To answer my own questions in order, I'm thinking 1) Not much more  popular than it is now; 2) probably not; 3) The good folks at Paizo  might 
want to but it might not serve Pathfinder if D&D death spirals. 
D&D has the name brand and, as some have said, the name matters. If D&D  advertises more broadly and sells the Red Box in Target, it is more  likely to find new players than if Pathfinder does the same because no  one outside of the RPG community has any idea what Pathfinder is. In  other words, we shouldn't underestimate the power of the name brand  "Dungeons & Dragons," and we need that name to have any chance of  growing the hobby, partially because to everyone outside of the hobby, the two--RPGs and D&D--are synonymous, like Kleenex and tissue paper.
Another thing to keep in mind is that a  relatively small number of people are responsible for a large percentage  of RPG sales. So unless WotC (or Paizo) is somehow able to bring in a  substantial number of new players, we're going to have the same core  consumer base in ten years as we have now. And I think we shouldn't fool  ourselves with just how small that consumer base is; sure, maybe a few  million people world-wide play table-top RPGs at some point within any given year, but how many of them buy books? Maybe half or less? And how many of those people buy more than one or two books?  A much smaller number, I would imagine. And how many buy books  regularly, on a monthly basis? I would guess it is a five-figure number.
To put it another way, a very small percentage of the total gamer  population (certainly less than 5%) purchases a large portion of the  published product (I would guess at least 50%). In order for the RPG  industry to maintain its current level and thrive, that population has  to keep on buying; furthermore, that population has to replenish  itself as it gradually dwindles through attrition, "retirement", and  even death.
Given that the dominant gaming group is Generation X (born in the 60s  and 70s), this core should remain relatively stable for the next ten,  maybe twenty, years. Beyond that, who knows. But the next largest generation, "Gen Y" (born in the 80s and 90s) is not nearly as big, and the third, the Boomers (born in the 40s and 50s) isn't getting any younger.
To get back to my initial questions, my sense is that Paizo's best chance of continued success is that if A) D&D flourishes (and thus RPGs in general flourish), and B) enough fans of D&D become disenchanted or bored and find Pathfinder. Paizo can't do anything about the first, except cross their fingers and pray that someone takes charge of the floundering ship called 4E; but they 
can continue to create excellent products and also an easier gateway product (which it sounds like they are doing). But no matter how great a starter kit they put together, unless it has the words "dungeon" and "dragons" on the cover, it has very little chance in bringing in the numbers that are needed to grow the hobby.
But if Paizo veers from that course and starts focusing on dethroning 4E, I think they'll only hurt themselves in the process. After all,  without D&D there would be no Pathfinder (which is a form of D&D, after all) -- this is not only true of the past but probably the future.
As an aside, here's a strange thought: What if Ryan Dancey is right and  D&D death spirals to the point that WotC drops it and a growing  company named 
Paizo buys it. Then 
Paizo releases a little game called  "Dungeons & Dragons 5th Edition," which is essentially Pathfinder 2E. OK, it  probably won't happen but it 
could (right, Lisa? 

)