I don't think it's controversial to say that a lot of the best work is done under significant constraints. Look at George Lucas and his body of work. Once he could do anything he wanted, and he didn't have to come up with creative solutions to get around hard constraints, his work got significantly worse. You can say the same thing about the Matrix 2 & 3 & the Wachowskis. I'm honestly not trying to disparage Lucas or the Wachowskis, they've done brilliant things - the point is simply that people work better when they have to work within constraints.
Part of it is the pressure - you rarely have as much time or money as you need, or you don't have whatever things you want (buttons for action games on iPhone, for instance), and so you need to be creative. But it's not just the creativity - it's the focus. When you don't have all the resources you want, you have to keep thinking about the thing that you're making and figure out what you have to cut, and what you absolutely, positively cannot live without.
Forcing yourself to continually ask that question, and then make the version of it that fits within your constraints makes what you're building better. It's extraordinarily rare that your first idea is the best one, and in a case where it's simply a subjective decision, if Lucas has an idea and someone says "maybe that's not great", it really doesn't matter, Lucas gets what he wants. On the other hand, it Lucas has an idea and he can't get it to fit within a limited budget, it doesn't matter what Lucas wants, he can't have it. Or he has to assess what he wants to lose to get it, or what he wants to get in exchange for losing this.
It's very hard to make those kinds of calls unless you're up against actual pressure. Simulating a situation where you want to give up something you really, really like for something you love isn't the same as having to give it up.
So one thing that constraints can help with is focus & efficiency.
The second thing is that sometimes, you believe you're not in a box when you actually are.
I really, really like Super Evil Megacorp's game Vainglory. I know some people who've worked on it, I've played it a bunch, I've even paid for content. I think it's a brilliant execution of a MOBA for a touch interface, simplified in many of the right ways for accessibility and ease of use, and it's one of the prettiest, most ambitious games I've ever seen on mobile. But it has, I think, a fatal flaw, and it comes from the fact that they didn't think they were in a box when they built the game.
Hardware has certain constraints. You have a certain amount of processing power you can deal with, you have certain forms of input that you can take. But you're also constrained by how people use that hardware and what their expectations & habits are. The critical flaw in Vainglory is that the games are 20-30 minutes long, and they're unable to be interrupted.
If you look at mobile games, "session length" is a thing that's often measured as a way to see if people are "engaged" with your game. For me, practically speaking, my average session length when playing a mobile game is about 5 minutes. It rarely exceeds that these days, and if a game expects a longer commitment from me, it's a barrier to entry. I've had X-Com: Enemy Unknown taking up 3 gigs of space on my phone for the better part of a year. I want to play it. I bought it with every intention of playing it. I already know (because I played it on my 360) that it's a great game. I've played it exactly once. And for how long? Five minutes.
The problem is that this is how I use my phone. I play games on my phone in very specific circumstances. When waiting in line. When waiting for food. When waiting for someone else to show up. In the bathroom (sorry, I don't mean for that to be TMI, but practically speaking, this is where a LOT of mobile gaming happens). Worse, if I don't feel like I can make progress in the time I can allocate to it, I won't even start playing. Double-worse, if I have to suddenly quit (and I think a huge percentage of mobile gaming experiences end abruptly), if I lose my progress or am punished, I resent the game for not respecting my time.
So I've been using my phone to play games now for about five years. And my average session length is about five minutes. A single game may change that, but the games that have changed that for any degree of time do so by giving me an experience I can enjoy in <5 min that I want to have over and over again. And once I feel like the game is pressuring me to play longer, I quit.
So as much as I love Vainglory, or as much as I want to play X-Com, the problem is that those games weren't built with how I use my phone in mind. In this case, they're asking me to figure out how to break out of the box, but the problem is that I don't have to break out of the box, I only want to - and it's very, very difficult to break the box unless you absolutely have to.
So first, you have to know what the box is. You have to respect that there is a box, and that you're hugely unlikely to be able to change the box. So start your game's design with it fitting in the box. Start with the constraints, and understand that it's not just about making do with less, it's about the pressure forcing you to constantly make your game a better experience for your players.