For a typical simple monolithic web application which is likely to be the only client accessing the database, is there any value in using a dedicated schema that is not the default public?
As already pointed out, some use schema as a namespace feature.
Also within a very large monolithic app you might still want some separation of access given to different modules, so a nasty bug that allows injection or inspection attacks has a more limited scope for causing DoS or exfiltration. You can control access on a per-table basis or even per column in some DBs, but the schema can be a convenient place to configure that over a larger surface in one go.
How useful any of this seems to you is going to be a subjective thing.
IMO, no. Public is just what is there by default and you could replace that with anything at the cost of having to configure the search path. Not worth it unless you are going to use multiple schemas anyway.
It's useful to have multiple schemas during development, and to allow the database owner to manipulate them, and not require superuser for these tasks. It's great that this will now be the default.
It will make some of my DB initialization scripts easier. Currently database owner can't even remove the public schema in a new database, because it's owned by postgres role.
I regularly make differently named copies of schemas and switch between them just by altering the search path in the app, just to try out some modifications or to run testsuites. You can drop and recreate an entire schema in a single transaction without the app having to close connections to the database at all, etc.
It's useful for so many things, where grouping some DB objects together has benefits.
It reminds me how Elasticsearch changed their default index shards number form 15 to 5.
Overall, I feel like decent software that is used by millions of devs can afford being "a bit hard" in the quick start/first interaction stages.
Look at how many articles there're about intro to something, and how many about real/production cases. People leave default configs, so I find it wise to make those restricted.
Can't even imagine how many products are running with software on the default settings that are not supposed to be used in real life setups
I feel the same way. Default setting should be secure, unsurprising and suitable for at least small-time production, and good software further guides the user to use it such that they aren't likely to shoot themselves in the foot.
Unfortunately, it seems quite often software defaults get optimized for developer convenience and may do insecure things like installing development-time dependencies by default...
When someone goes and uses that software in production, they are very likely to end up using the bad defaults. That is not the user's fault.
If you can't provide at least secure defaults, the software should not run at all until the user has made the necessary choices.
Wow I didn't know that nor I even expected it. Can you recommend me a way to achive this behavior (i.e not allow users without permissions to create tables in the public schema) in Postgresql 13?
you can change the permissions for the default schema after databas ecreation, or change the permissions of the default schema in the template database that is used when you create a database