Why don't in-flight entertainment systems have the capability to connect to our own devices and play movies?
The answer is that they do. These are actually quite common in the U.S. and many other parts of the world and have been so for at least a few years now. All of Delta's recently-acquired or upgraded interiors on anything 737/A320 size and up have this, for example. Most of Cathay Pacific's fleet and, IIRC, all of Korean Air's fleet also had IFE systems to which you could connect your phone or tablet (via USB.)
As far as the Wi-Fi concerns mentioned in another answer, much of the world does not have any problem with Wi-Fi or Bluetooth being enabled during flight. Nearly all major U.S. airlines offer Wi-Fi during flight and some of them even provide it gate-to-gate (that is, including taxi, takeoff, and landing.) Most of them offer streaming media (movies, TV shows, and even streaming live TV) over the Wi-Fi that you can watch on your own device. On Southwest Airlines, this is actually their sole form of IFE service. There are no screens in the seatbacks; you just use your own, which is almost certainly better quality anyway. Another benefit of this approach is that airlines don't need to constantly upgrade their IFE systems, as passengers will effectively do that for them when they buy new phones/tablets/laptops.
There do exist a few jurisdictions around the world where Wi-Fi/Bluetooth are still not allowed during flight, but these seem to be a minority now.
Are there any regulations that prevent engineers from designing innovative in-flight entertainment systems?
There are no regulations banning them, but there are lots of regulations that make them expensive to design, test, and certify for flight (as with anything else that is installed on an airplane.) To underscore just how expensive new IFE system testing can be, GoGo (a major in-flight Wi-Fi provider) actually has their own 737-500 (registration N321GG) that is used for nothing but testing their in-flight Wi-Fi systems.
Even once the design, testing, and certification are done, it's expensive to take the airplane out of service long enough to install the new interior. Keep in mind that most airliners will be generating hundreds of thousands of dollars in revenue per day (although much less in profit, of course.) Roll-outs for new equipment will generally be multi-year processes for large airlines just due to the shear number of airplanes that must be modified and that fact that you can only take a few out of service at any given time if you want to keep your airline operational.