My coworkers seem much more interested in making a bigger EMR or adding nodes to Redshift than designing a reasonable data mart because "star schemas don't scale". I'm interested to see what you come up with, it is a huge gap in the current literature.
Shameless plug: http://github.com/socialpoint-labs/sqlbucket
What is really good is to assemble a library of visual queries for the customer. This is a good idea for the reason that many users have the same fundamental types of queries on their data. When finally you have enough of the basic queries that the user can do useful work without programming then you can find a way to customize this yes.
Have you data on how many similar queries customers use? Then you should know how to create the basic set of important operations.
So what you describe is somewhat built in to what we have now. Users still have to choose what columns they want to look at (there's no real way for us to guess that) and then we do apply some knowledge on what type of data they're looking at to help them get to what they're likely looking for.
We've also tried at times to make default dashboards for data sources when people connect. We can do this to some extent with known Schemas like connecting GA, SalesForce, Hubspot, etc, but for databases - that's proven to be a largely impossible task so far. Everyone's data is so different, and have such odd conditions to consider filtering by, that the auto dashboards end up being quite useless.
Finding out the distinct set of values in any column helps a lot, referential integrity helps a lot, but without those queries its pretty dang hard.
https://dataschool.com/data-governance/
Our next phase is to help people get to that cleaner source of truth much more quickly than traditional dimensional modeling approaches. Tools like Visual SQL and DBT (https://www.getdbt.com) are really changing the complexities here.