One obvious problem is that the semantics of a DSL arent extendable in that DSL, making it highly brittle. So, eg., with parsing, as soon as you need bespoke syntax-error handling, etc. etc. you're leaving the world of any DSL you can create. Since "bespoke" here will, ultimately mean, a semantic specialisation that no generic DSL will support.
At the point where your DSL enables these abitary specialisations, it is just the host language.