The key difficulty is identifying what these are is far from obvious upfront, and so often an index appears adjacent to a table that represents what the table should have been in the first place.
This is why I fundamentally find SQL too conservative and outdated. There are obvious patterns for cross-cutting concerns that would mitigate things like this but enterprise SQL products like Oracle and MS are awful at providing ways to do these reusable cross-cutting concerns consistently.
> Good programmers worry about data structures and their relationships.
> -- Linus Torvalds
I was specifically thinking about the "relationship" issues. The worst messes to fix are the ones where the programmer didn't consider how to relate the objects together - which relationships need to be direct PK bindings, which can be indirect, which things have to be cached vs calculated live, which things are the cache (vs the master copy), what the cardinality of each relationship is, which relationships are semantically ownerships vs peers, which data is part of the system itself vs configuration data vs live, how you handle changes to the data, (event sourcing vs changelogging vs vs append-only vs yolo update), etc.
Not quite "data structures" I admit but absolutely thinking hard about the relationship between all the data you have.
SQL doesn't frame all of these questions out for you but it's good getting you to start thinking about them in a way you might not otherwise.