My personal opinions:
1) Although Gracie/Brazilian Jiu-Jitsu began as a mostly Self Defense oriented art, there are actually 3 versions of BJJ; a Self Defense version, an MMA/Vale Tudo version, and a sport BJJ/submission grappling version.
With the explosion of the sport of BJJ/submission grappling worldwide there has developed a large market for offering classes pertaining to such. Likewise, MMA has also grown significantly in terms of popularity and exposure and thus there is also a pretty big market for offering BJJ classes that translate to MMA.
It seems that the aspect of BJJ that is least addressed these days is the Self Defense aspect and in fact many schools never teach any of it (or if they do, it's an after/passing thought). There is an ongoing effort on the part of people like Rickson, Pedro Sauer, and Rener/Ryron to revive the Self Defense aspect of BJJ, but since there is really no single universal "standard" for what is taught, instructors are free to teach what they want to/feel will bring in (and keep) the most students into their classes.
So, it's not that uncommon that your instructor mostly focuses on the more sportive applications. It doesn't necessarily reflect his knowledge base or efficacy as a BJJ instructor, just perhaps signifies that he either feels that doing/teaching the way he does is the best way to keep his school going, or perhaps that he is more knowledgeable in the sportive aspects (which again, doesn't signify that he isn't a "good" BJJ instructor).
2) Some schools have structured requirements for belt promotions, others don't; again, there is no universal standard.
It's also important to understand that you can't really judge everyone by the exact same standards. For instance, let's say you have a 50 year old professional man who has a full time career, some nagging injuries, and is not particularly athletic and a 20 year old HW Division 1 NCAA All American wrestler who start at the same time. Do you really think that the 50 year old is going to be tapping/keeping pace with the wrestler at any point in their BJJ career? No, they're most likely not and you cannot really expect that 50 year old to keep pace with the 20 year old (unless maybe the 20 year old stops doing any athletics for the rest of their life and the 50 year old religiously attends classes and does everything in their power to get as good as they possibly can; then maybe in a pure Gi BJJ context they might catch the wrestler at some point).
You also have to take into account injuries/physical limitations, sex/gender, and just plain natural abilities/talent. Even though BJJ prides itself on its effectiveness, anyone who tries to tell you that attributes don't still greatly affect the outcome and experience of any grappling match is flat out lying to you. Yes, skill can potentially make up for or even turn the tide in the favor of the physically inferior individual, but the discrepancy is going to have to be much bigger than if it were two equally physically matched foes.
And don't worry too much about it only taking 2 years to get to Blue Belt; Blue Belt does not generally represent any great accomplishment in terms of skill gained, it generally just means that you pretty much look like you have some idea of what to do when rolling and aren't just spazzing around when on the mat, have some idea what to do in the common positions (both offensively and defensively) and prop have a few subs that you have gained some level of proficiency with. If it was 2 years to Purple Belt, then I'd say to be concerned.
3) As contradictory as it seems to what I said in point 1, most people are not interested in competing. Most people who do BJJ actually just enjoy the art, want to get in some exercise to help them stay in shape, enjoy the self improvement and community. My head BJJ instructor actually ran an open BJJ poll not too long ago and competition was actually towards the bottom of the list of priorities (when all answers were tallied up). Yes, there are people who enjoy it and want to pursue it, but they are in the majority as far as the entire BJJ community goes.
And, just to note, my instructor is a former World Champion, Multiple time NAGA champ, has won multiple other competitions, is Glover Texieria's BJJ coach, and has quite a few very successful competitors (in both MMA and Submission Grappling/BJJ) who train under him, so I would definitely not classify him or his school as "casual".
4) Whether you choose to change gyms is going to come down to whether you feel that you are getting what you want out of the school you are currently training at. Just like not every car is going to "fit" every individual who test drives it, not every BJJ school/instructor is going to "fit" every student who tries out the classes.
Staying where you are not happy just for the sake of "loyalty", while perhaps admirable from an integrity standpoint, will in the end only wind up creating resentment and is unlikely to end up seeing you stay for the long haul.
So, I say try out the other school if you think those other logistical changes are feasible and see how it "feels" to you. If it's a better fit, then switch gyms. If not, at least you'll know that the "grass isn't greener" over there and you will likely be more at peace with your decision to train at your current school.
Finally, your instructor is correct in that Jiu-Jitsu is Jiu-Jitsu from the standpoint that the same principles underly all grappling arts (be that Japanese Ryu's, Judo, Sambo, Small Circle, all Brazilian Jiu-Jitsu, etc...). The differences make up the "art" portion of all Martial Arts and that is where all the variation in terms of exactly how techniques are executed, to preferences of subs/escapes/passes/etc..., to strategies, to Belt requirements, to "priority of techniques" based on chosen arenas of application,etc...
Hope this helps. Good luck.