I am curious if this is other folks' experience as well, or do you actually throw out the MVP and start all over at some point? If so, at what point do you make the break?
Premature scalability is as dumb as premature optimization and premature generality.
Hell, in clojure I usually develop against a hash-map of hash-maps stored in-memory until the project gets far enough to re-implement the data layer (which I've hopefully abstracted well enough to not be a big deal).
Think of Mongo less like a schemaless postgres, and more like a persistent redis. Ease-of-use is its true advantage, and I think anyone who exceeds its capacity should be happy to have the problem.
Plenty of personal projects end up running on Mongo, because it has a rich query layer for quick hacking. I also never expect these to exceed the amount of RAM on my machine either.
I've worked for 15 years with relational databases and for the recent 6 months with mongodb on my startup. For me, the agility of not having to define my data in advance, and "work" so much to explain the DBMS how my schema should behave is no less than a game changer in my ability to build the MVP quickly. I just can't imagine having to invest all the labor in having to model everything I did with a normalized database and ORM.
And nowadays it is so easy in a datamodel in a RDBMS to make changes. It is high flexible too.
But another worst thing in Mongo is the performance at complex queries. It is a nice bin for thinks nobody needs or to put documents in but that's it with Mongo.
I would start with MongoDB, get a grip on what on earth the product is doing, finalize the schema on the fly based on A/B tests, customer feedback and analytics, only once the schema is finalized move it to a SQL database if needed.
If you are not using a good ORM + DB migration system, then MongoDB will make perfect sense when you are quickly iterating through ideas and trying to find a product / market match. You really have no clue how your data schema is going to look like in the end, why confine it at the start? the vast majority of startups sadly won't get even near the phase where they really reach scale related performance issues, so choosing MongoDB for prototyping your business absolutely makes sense to me.