MIDI Tutorial
Byron J. 
Shortcomings
MIDI was quite successful in solving the initial problem: synthesizers from different manufacturers can communicate performance information. A performer can connect MIDI instruments, and they respond similarly. Simply being able to do that was revolutionary, and paved the way for widespread adoption of MIDI.
It's popularity has been a mixed blessing. As MIDI caught on, it's been revised and extended, gaining features far beyond the initial intent. In hindsight, some of these features might be overly cumbersome or anachronistic. For example, we can ship files to and from MIDI instruments using SysEx messages, but today it might be easier to build an instrument that accepts SD cards or USB thumb drives.
Let's examine a couple of the more common complaints.
The Piano Keyboard
MIDI is based on a digital representation of the piano keyboard, and it works well for instruments that ordinarily feature a keyboard. Note on and off commands have an obvious correspondence to actuating piano keys. How they relate to how other instruments is less obvious.
As one specific example, translating a guitar performance into MIDI data is particularly tricky. Accurately converting the vibrations of a guitar string into MIDI note numbers is much harder than simply noticing that a switch has closed. While there are commercial MIDI guitars around, they're best approached as a unique instrument, not a simple replacement for a guitar.
The piano keyboard is also intrinsically linked to the 12-tone western chromatic scale. How scales from other cultures translate into MIDI is not always obvious. There are System Exclusive messages that transmit alternate tuning information, but their implementation is uncommon.
Digital limitations
MIDI was designed using digital technology that was inexpensive in the early 1980's. More than 30 years later, it's still being used. Many other digital technologies from that era have since disappeared -- remember 5 1/4" floppy disks and monochrome, text only displays?
Computer networking has matured considerably during those 30 years. When compared to modern protocols like Ethernet or USB, MIDI is extremely primitive. The links are unidirectional, there is no provision for data integrity checking, such as a checksum or CRC, and addresses (channels) must be manually configured. The 31,250 bits-per-second links are also comparatively slow.
The flip side of this coin is that that MIDI is easy to implement on a modest microcontroller system. Serial port peripherals are found on many MCUs. The low data rate means that it's hard to overwhelm a receiver with too much data. Since the messages are small, storing them doesn't require much memory.
Within the messages, there are many places where the underlying data formats are also constrained.
With four bits of channel data, a MIDI buss supports a maximum of 16 channels. The usual workaround for this is to run more than one buss.
Many of the values sent by MIDI are constrained: key numbers, continuous controllers, and aftertouch values are all 7-bits long, allowing a range from 0 to 127, which can be too coarse for some parameter values. MIDI has provisions for pairing continuous controllers as an MSB and LSB to form 14-bit values, but in practice this is uncommon.
In examining the output of one commercial keyboard controller, the bender was actually only sending seven bits of data, left justified in the 14-bits of the bender messages. Moving the wheel slowly results in audible stairstepping. This is probably the resolution of the underlying ADC, an onboard peripheral of the system's MCU.
MIDI just didn't leave itself much room to grow.