All of these are mostly issues with the database engine implementation:
1. "FKs are in your way to shard your database." => not a problem for distributed databases that can query and duplicate data across shards/servers; alternatively, if the referenced data just isn't there in the database, a foreign key is not usable by definition
2. "FKs are a performance impact" => the app either just got the foreign key value from the database, so it should be cached in memory in a properly implemented database engine, or otherwise, the application relies on the database checking so you need the foreign key for correctness
3. "FKs don't work well with online schema migrations." => not a problem with database engines that properly support online schema changes without locking, downtime or table renaming hacks
The performance impact is at write time, and having the data cached in memory is irrelevant. It's the locking overhead that's non-trivial, especially if each table has several FKs, when operating in a high-volume OLTP environment.
As for "database engines that properly support online schema changes without locking, downtime or table renaming hacks", please name some. In my experience, every major DBMS has cases where certain ALTERs block concurrent DML, which is extremely problematic on very large tables. Or even cases where there's no locking, but the operation still takes a very long time, which is conceptually problematic for logical replication.
1. "FKs are in your way to shard your database." => not a problem for distributed databases that can query and duplicate data across shards/servers; alternatively, if the referenced data just isn't there in the database, a foreign key is not usable by definition
2. "FKs are a performance impact" => the app either just got the foreign key value from the database, so it should be cached in memory in a properly implemented database engine, or otherwise, the application relies on the database checking so you need the foreign key for correctness
3. "FKs don't work well with online schema migrations." => not a problem with database engines that properly support online schema changes without locking, downtime or table renaming hacks