Vitess deployment comes at a cost:
1. You can't have single database view of all shards 2. No distributed ACID 3. No distributed JOINs
If I were to do it in PostgreSQL 14 natively without any other third party plugins, I can get help of Table Partitioning (say root server) + Tables on Foreign Servers (say leaf servers) through FDW. Parallel scans and JOINs are allowed. Also, PostgreSQL 15 (in beta now) will allow parallel commits to foreign server tables through FDW.
I wish you all the best in operating that at scale and providing a reliable general purpose PostgreSQL DBaaS (even if only internally) around it. :-) PostgreSQL is great, not going to argue otherwise -- every solution has tradeoffs and if the tradeoffs of one solution fit your usage best then go with it. If you need to scale out and manage a large cluster of PostgreSQL instances as if it was a single logical database then I'd recommend something that's in a similar space as Vitess and PlanetScale -- Citus and Citus on Azure respectively. At the hand waving level it's always easy to "do this, and that", but it's a whole other matter when you develop a general purpose production-grade product that anyone can use and operate at virtually infinite scale. :-)
Look, I get it, you have to sell your product. Some folks want semi-infinitely scalable storage, and they don't understand that the only way to achieve it is turning their DB into a key-value store. As a side effect they would have to rewrite their whole application from scratch, but they would only realize it after they get vendor locked in.
You can advertise your solution as MySQL-compatible. And I can claim that it's dishonest.
OK. You're the only one talking to this straw man though. :-) Every Vitess user that I'm aware of has a pretty typical 2NF/3NF schema design. A small sampling of them being listed here: https://vitess.io
You setup your data distribution/partitioning/sharding scheme so that you have data locality for 99.9999+% of your queries -- meaning that the query executes against a data subset that lives on a single shard/node (e.g. sharding by customer_id) -- and you live with the performance hit and consistency tradeoffs for those very rare cases that cross shard queries cannot be avoided (Vitess does support this). You should do this even if the solution you're using claims to have distributed SQL with ACID and MVCC guarantees/properties. There's no magic that improves the speed of light and removes other resource constraints. In practice most people say they want perfect security/consistency/<name your desired property here> but then realize that the costs (perf, resources, $$, etc) are simply so high that it is not practical for their business/use case.
I know MySQL fairly well (I started working at MySQL, AB in 2003) and you can certainly claim that "MySQL-compatible" is dishonest but I would offer a counter claim that either you don't know this space very well or you're not operating in good faith here.