If RSA is limited to 117-200 bytes or so, is that a very limited use case?
In practice, asymmetric algorithms like RSA are usually used for key transport. In other words, instead of a true message, they are used to encrypt a secret key for a symmetric cipher.

That symmetric cipher key is used to encrypt the actual message, and that could be gigabytes, depending on the algorithm. 

Standards like TLS, PGP, and S/MIME use RSA in this way.

By the way, a limit of 117 bytes is for a 1024-bit RSA key. Keys that small are no longer recommended.