Sharding has nothing to do with high-availability.
And primary-secondary failover in my experience is rarely without issues.
There is a reason almost every new database aims to be distributed from the beginning.
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And to respond sibling comment about "noticeable" downtime....
Primary-secondary failover in <1m is very feasible. And each minute downtime is a mere 0.002% for the month.
Primary-secondary isn't what is hurting your availability.
And given that the entire industry has moved to a distributed model despite its complexity gives you a hint as to which way the wind has been blowing for the last decade.
Failover is automatic for PG when using e.g. Patroni. Of course you lose active transactions and that might be a showstopper, but monitoring failover? I am curious when you'll have to do that.
That's partly because you can't compete with the existing RDBMSs if you're single node: they are good enough already. Nobody will buy your database if you don't introduce something more novel than PostgreSQL, whether that novelty is worth it or not.
And there are four major reasons still to choose MongoDB over something like PostgreSQL.
a) PostgreSQL has terrible support for horizontal scalability. Nothing is built-in, proven or supported.
b) MongoDB has superior ability to manipulate and query the JSON.
c) MongoDB is significantly faster for document-attribute updates.
d) MongoDB has better tooling for those of us that prefer to manage our schema in the application layer.