Problems: Difficult to maintain due to bad granularity and monolithic approach. Unable to extend from the game side.
Alternative: Shader compositing. In OpenGL you can extend the functionality by either linking with different shader objects, swapping the subroutines, or by directly modifying the source code.
Problems: Very limited BRDF support. High fill-rate and GPU memory bandwidth load. Difficult to properly support MSAA.
Alternative: Tiled lighting. You can work around the DX11 hardware requirements by separating lights into layers (to be described).
Problems: Difficult to decompose into position/rotation/scale. Take at least 3 vectors to pass to GPU. Obligation to support non-uniform scale (e.g. no longer skipping invert-transpose on a 3x3 matrix to get a normal matrix).
Alternative: Quaternions and dual-quaternions. Both take 2 vectors to pass.
Problems: Bug-hunting is difficult because of bad problem locality. Assumptions over the context are easy to make, but if you decide to check it with assertions, why not just pass the whole state instead?
Alternative: Provide the whole state with each draw call. Let the caching work for you.
Problems: Memory management and safety. Compiler-generated copy operators/constructors. Pain dealing with headers and optimizing the compile time. Many many lines of code.
Alternative: Rust. Other "safe" languages (.Net family, Java, Python) are not as low-level and often trade performance for safety (i.e. global GC phase causes an unacceptable frame rate interruption).
All I actually know is that there is a thousand and one difficult architectural issues of the graphics engine, and there is no silver bullet to most of them. For the most common solutions I listed possible alternatives, but they are no near being flawless. I hope that one day the amount of experience I get will magically transfer into the quality of my decisions, and I will finally know the right answers.