Maybe it depends on the application, but web servers are effortless with something like axum. Libraries can do a lot of heavy lifting to expose straightforward coding patterns. Never had any problems like you desribed with database connections and such. In rust with db pools things just work and get closed on drop etc. I would never even consider making a higher order function for that.
Only other language that I think gets close to rust ergonomics is Kotlin, but it suffers from having too many possibilities for abstractions.
Depends very much on the market.
On my line of work we don't do Web servers from scratch, we use lego pieces like with enterprise integrations.
Think Sitecore, Dynamics, Sharepoint, Optimizely, Contentful, SAP, Mongolia, Stripe, PayPal, Adobe, SQL Server, Oracle, DB2,.....
Axum offers very little over existing .NET, Java, nodejs SDKs provided by those vendors.