Unfortunately, APIs exposed by MTP are very different from a normal filesystem APIs. Therefore exposing MTP device as a read/write filesystem is not possible. The main reason:
Neither the MTP nor the PTP standards allow for direct modification of objects. Instead, modified objects must be reuploaded in their entirety, which can take a long time for large objects. With PTP/MTP, the file size must be known at the opening stage.
Your common file copy program just opens a source and a target file, and copies data in chunks from the source file to the target. This won't work with MTP, since you need to use MTP special functions, and generic filesystem primitives (read, seek, write) are not available.
There are also other limitations. For example, the number of files that can be read or written simultaneously on an MTP device is severely limited. The device simply does not behave like a filesystem.
I suppose read-only filesystem driver for an MTP device might be possible, but because of the problems outlined above, it will be of very little use, so nobody bothered to create it.