I realize that this question is probably asked from a 'disadvantages compared to other bench/handheld DMMs' and my answers don't reflect that, but for me one of the big disadvantages are:
1) Display is attached to the meter, and sometimes I want to be able to look at the meter value and the probes at the same time (though I solved this with a SCPI script on my laptop)
2) To my knowledge, pretty much every bench DMM is HIGH-Z (usually >1 GOhm) input impedance only on the 10V range and below. If you want high impedances at higher voltages you need either electrometers, or SMUs.
3) While bench DMMs can often measure quite small voltages, measuring small currents is hard. A TIA-based front-end such as some electrometers or pico/femto-amp meters would be awesome (and is still one of my projects but haven't finished it yet)