You think it's so simple right? Just raise the cap? Just raise the time limit. Everything else will be fine right? But it's not so simple.
You talk about competitive play like it's this simple blanket attitude you can apply to anything. But there are many ways to foster a competitive spirit for a game. The more you understand the style you're going for (or the style others go for) the easier it is to see how the philosophy affects the rest of the design.
Coin Rush is a great mode. But it's secondary to the main game. So really, it's building on the design we already understand about Mario (I only assume you understand). If not... read up...
http://critical-gaming.com/blog/2009/11/19/the-measure-of-mario-pt1.html
Mario, with its very well tuned, layered, skill-based gameplay works best with repetition. All the possibilities and emergent happenings are revealed the more you play and play through the levels. Coin Rush is a brilliant way of encourage people to play through again who might otherwise have beaten the game once and put the game away.
Coin Rush helps players focus on what's great about Mario's design which is its layered level design as you precisely platform through it. So the low time limit helps move players along. Similarly, the coin cap is designed to be high enough to strive for in most level combinations, but not so high that you can blow the "get 1 million coins" goal out of the water. This overall game goal is more important to the integrity of NSMB2 than a higher cap or no cap to the coin rush levels. The bottom line is the levels were tweaked for coin rush, but not designed for it from the bottom up (at least initially).
http://iwataasks.nintendo.com/interviews/#/3ds/nsmb2/0/3
So with the focus on what Mario has done the best since the 80s, coin rush was born out of these design goals. The cap gives us a nice mark to aim for, but the point is to enjoy the level design and play through the stages repeatedly in random combinations.
Just because you can imagine what the game would be like without the cap doesn't mean that it would be better overall. Nintendo obviously weighed out the gain in competitive score chasing with what they'd lose in terms of the core Mario design/gameplay. And what we have now isn't necessarily less competitive. It's just different. If you want to prove your skill, then 30,000 ever level pack or at least beat every single other score out there. If you want to be the best of the best, then record your videos and do the math on your own scores. Obviously, Nintendo designed Coin Rush to encourage re-play and grabbing coins, which is why the street pass sharing is the only way to share your scores in the game. I'm not even sure how extensive the leader board is for the coin rush DLC pack 2.
Laugh it up if you want. I just gave a talk at a Game Design Conference basically explaining why many who think they're game designers are really just pitiful dreamers. Do your own gut check if you want.
Bizarre cap? I bet, Nintendo counted how many coins are in the levels and factored that data in with the flag pole multiplier. Then with the results, they figured the only way to get more coins than that is to abuse something in the game like spawning or koopas. So, not wanting to discourage that play entirely, they put the cap at a nice number so that the cheap strategies can get there and also some straight up tight gameplay. The 30k cap is actually quite genius, and I can see that it's working from the comments in this thread.
Easily? Huh? I where's all the videos of people easily surpassing the total without using the cheap Koopa strategies on vines/stairs?
I haven't seen many besides my video. The few that I've found simply abuse spawn loops to a high degree. That's basically how you get the score; on the first level just abuse spawns or koopa trick. And you want to cap raised so that people will abuse these few strategies even more? That's really not the point of playing Mario. So to prevent this kind of "do whatever it takes to win" attitude from going too far, they placed the cap on the levels. It's really simple.
You guys are way too focused on the maximum score and not what the mode was designed for and how Mario gameplay works best.