Not to put too fine of a point on it, but it is never a good idea to use textures larger than 4096x4096. Memory (in all applications, including your operating system) is handled in blocks. The larger the blocks, the harder it is to manipulate the data efficiently. Small chunks of data can be scattered around your system’s memory as needed, and it takes less time to move these smaller chunks around. A large block can only be moved all at once, takes longer, and has fewer places that it can be placed.
In other words, keep your blocks small.
With textures, that translates to using several smaller textures rather than one larger one. For example, sixteen 2048x2048 textures have exactly the same number of pixels as four 4096x4096 textures or one 8192x8192 texture. That means that you can get exactly the same level of detail. But the 2048x2048 textures will be handled much more efficiently than the 8192x8192 texture. This translates into smoother performance by your computer and software.