I think this aspect is often overlooked in the MVP discussion. Customers are trained to have certain expectations fulfilled and when they're not met they perceive things as broken, as you observe.
I think the examples of MVPs that have worked best appear to be targeting other startups or folks in the industry with a high degree of tolerance for failure and understanding of how this all works (and therefore patience with the process).
But most real-world customers end up disappointed with this kind of thing. So far as I can tell a lot of MVP-driven startups just accept that they'll lose a percentage of their early adopters over this.
Worse, and I have some experience of this with a startup of my own, often MVPs come with the need for investment $$ to make them truly viable. So what to do? Well get 10,000+ folks signing up and using your system, in just a few weeks, and showing it's got great demand (that was a big number for the space). Yet the more you ramp up early adopters the bigger the cliff when you still hear crickets on the funding trail and never manage to afford to give those customers - many of whom have invested a lot of time and energy in your product - what you promised them.
Many folks are okay with this. There's something almost sociopathic about many young inexperienced entrepreneurs who don't appear to think about the real world consequences of abandoning their early adopters (and their efforts and data).
> I think the examples of MVPs that have worked best appear to be targeting [...] folks [...] with a high degree of tolerance for failure
Yes. This is true for almost any groundbreaking product. The book Crossing the Chasm is the classic work on the topic. Almost any startup should seek out an early-adopter audience of people who need the product so much that they're willing to put up with flaws.
One thing more startups should do is narrow their marketing to the early adopter audience. Everybody else, you try to defer until you have a more solid product.