As long as you keep in mind that the "V" in MVP is viable and that viable is contingent on the nature of your product and market it is a pretty straught forward approach without a down side.
The "cons" start showing up when the perception of the product developer's concept of viable and the markets definition of viable diverge. For example I don't want to eat at a restaurant that serves the minimally viable food. No one I know is interested in a MVP pharmacutical. But in both of these cases the market reality of consumer expectation (or legal regulation) create the framework for the evaluation of" viable" from which" minimum" can be assessed.