This was intentional so that the CPU would support secure operating systems. In a secure operating system with rigorous memory access protections you could not allow any software - user or kernel extension or driver - to switch back to the full freedom of real mode.
They had a lot of interesting memory management hardware on the '286: rings and call gates - swiped nearly directly from the most secure hardware/software platform of the time: Multics. And they had new extensions too: task segments and task gates for multiprocessing.
These features never got used as they wanted. One major reason was that due to compatibility with all the peripherals - including disk controllers and graphics hardware that in those days were nowhere near sufficiently standardized - OS and other software that needed computer model/manufacturer independence needed to use the BIOS to access peripherals - and the BIOS was real mode - and the hacked-up switch to real mode (as discussed in other answers) was slow. Another major reason was that calling through call gates, and using hardware tasks, was much much slower than just implementing normal procedure calls and concurrent threads. Hardware task switching in particular was several times slower than just saving/restoring register context with normal instructions. So no OS software got written for these special modes.
These capabilities were also available when 32-bit processors were made - starting with the '386 (and they're still there in the x86 architecture to this day) - but with 32-bit addressing it turns out it is much easier to use paging hardware (address translation tables and so on) to get OS security - also much higher performance. No 32-bit OS used the stuff: Windows, OS/2, and all the Unixes used paging for process isolation and security.
I was actually saddened by this back in the day: I loved Multics, and the Multics architecture. The Intel designer's hearts were in the right place, and it was brilliant work sticking all that stuff in a commodity microprocessor, but it turned out to be the wrong solution for the problem. Operating system engineering had progressed past the Multics days and all that special hardware just did not lead to an economic solution.
