Embedded DSLs have much lower learning overhead, since they are just embedded in the language you are already using. Eg in Haskell, they are still valid Haskell programs. So they eg inherit the control structures from the host language, and most of the tooling in your editor, like 'jump to definition' also still works.

See http://wiki.haskell.org/Embedded_domain_specific_language

Because the overheads are lower, the payoff doesn't have to be as high to make it worthwhile.

(However, there's still some overhead, otherwise you wouldn't really label them as embedded-DSLs.)

The issue is that a good DSL shouldn't be a "language", it should be a tool, a textual UI that is designed by and for power users for a particular task. When you are doing something 500 times a day you want a hyper efficient tool to accomplish that. Learning curve is irrelevant, only efficiency and expressibility. A DSL is a great fit. If you are doing some task once a month you just want something simple you can wrap your head around quickly. The problem is that the former often forget that the latter exists and so recommend their workflow to everyone, forgetting they have different needs. But both sets of needs are valid.

I don't know. Eg people seem perfectly happy to use regular expressions for matching text, instead of accessing the same functionality via eg regular functions in their favourite language.