What limitations cause Shimano to stop at 11 gears and 409% overall ratio, whereas Rohloff can cram in 14 gears and 526%?
There are a couple of likely reasons IMO.
First, Shimano don't make anything like a Rolhoff and that's intentional. Shimano market strategy is all about mass sales to bike manufacturers, and expensive, complex IGH are not part of that. Even their spare parts - those sales are not a huge profit centre, but they do take a lot of staff time (even though their staff supply wholesalers). Their whole importer/wholesaler/retailer supply chain works like this, it's about supporting the sale of new bikes.
Whereas Rohloff stock spares for everything. Ring your Rohloff importer and ask, they will almost certainly go out of their way to help you, because that's the company ethos. But then, Shimano sell more top level groupsets than Rolhoff sell hubs. Rolhoff have chosen a market that Shimano ignore: the "buy it once" market. Few sales, at a small price premium. But loyal customers.
Second, the engineering is hard. This is not simple commodity manufacturing. Rolhoff make the machines to make the parts to build the hubs. They also have a really smart IGH designer who has been working on this one thing for twenty years. Shimano would have to put one or more of their really smart engineers on the design for a couple of years too. Instead of those people working on products that might actually turn a profit.
Note that you can't just copy a Rolhoff or any other complex machine. What goes in to the process is not what comes out. For, say, a gear, they start with a blank. How big? Only the maker knows. Then it's machined, with a special gear-cutting machine. Do Shimano have a machine that can make this gear? Maybe, maybe not. But they definitely don't know the exact design dimensions and tolerances. Then it's likely heat and chemically treated before final machining/polishing. Again, the details are important but you can't work them out from the final product.
Finally, given shitmanos reputation for briefly making short-lived crap, the Rolhoff market is going to look at a $1000 14 speed hub from Shimano (or 15, 16 etc) and say "how long is the warranty" and if it's the standard shitmano two years... They're going to snigger. Shimano would have to work hard to convince customers that they're even capable of offering a competitive warranty to the Rohloff one.
(I have owned a Shimano 8 speed hub... It failed after 5000km. Three times. So arguably 3 of them. After the last failure it couldn't be fixed because Shimano didn't support that model any more. A new wheel would have cost about a third as much as a new Rolhoff-equipped wheel. If I was stupid enough to fall for that trick again, anyway. By contrast, I have a low 5000's serial Rolhoff - 16 years old - that has been cheaper per kilometre and obviously much more reliable. The two hubs are not even trying to do the same job, except in the very broad "both are bike parts" sense.)
Making an internally geared hub with 14 speeds that is reliable is prohibitively expensive. A Rohloff hub alone costs than most people's bicycle. It is a hard sell to most people except for a few, making it a real niche market. There was nothing like it when it first came to market (must be over 20 years now), and once there it was the instant leader of a very small market place.
There is little incentive for most manufacturers to try to compete. Unseating Rohloff in such a small market is not the best business decision, and making is cheaper version of it is exceedingly difficult. The amount of complexity and tolerance is to get 14 gears is crazy. Shimano comes close with their 11-speed hub, which is their most expensive internal hub and if I'm honest it does not appear to be as reliable as the 8-speed version (I had the 11-speed hub for a couple years and had nothing but troubles).
The truth is it's a hard problem, it's already been solved, and there's not really feasible (yet) to do it for cheaper. This is why Rohloff is currently the only one.