Even in the case of a REPL, what you want isn't "interpret this string as code in the language in which this program is written and apply it to the state of the currently executing program". What you're really looking for is "interpret this string as code in language X and apply it to the state of the given sandbox".
The problem with using eval for a REPL is that you want an interpreter, but eval gives you unprincipled incremental compilation.
Javascript (and I'm sure other languages) is moving in the right direction with sandboxed evals, but those are very difficult to get right in an imperative language, where a lot of code relies on global state (e.g. the DOM). Purely functional languages solve this problem well by disallowing side-effects. Of course there remain the issue of unconstrained resource usage but this is much easier to solve.
The problem with using eval for a REPL is that you want an interpreter, but eval gives you unprincipled incremental compilation.
Javascript (and I'm sure other languages) is moving in the right direction with sandboxed evals, but those are very difficult to get right in an imperative language, where a lot of code relies on global state (e.g. the DOM). Purely functional languages solve this problem well by disallowing side-effects. Of course there remain the issue of unconstrained resource usage but this is much easier to solve.