The problem here is not with Rust's async design. It's that Rust has affine types and not linear types. This is not something that could have been solved with more work on the design. It is not that there was "a decision" to allow dropping tasks; it's a constraint on the design that the language requires. (Personally, I'm unsure as to whether a practical language with true linear types is possible, but it's worth experimenting with. Rust is not and never will be that language, however.)
The problem here is not with Rust's async design. It's that Rust has affine types and not linear types. This is not something that could have been solved with more work on the design. It is not that there was "a decision" to allow dropping tasks; it's a constraint on the design that the language requires. (Personally, I'm unsure as to whether a practical language with true linear types is possible, but it's worth experimenting with. Rust is not and never will be that language, however.)