In the context of programming language design, an unambiguous syntax is important. However, parsing technology is not exclusively applied to programming languages. Marpa's support for ambiguity and abstract syntax forests can e.g. be used for natural language processing. 10 in 10 joke tellers concur: Ambiguity in the English language is a feature, not a bug.
Well, when I use Marpa, I don't actually use abstract syntax forests. But the ability to generate and compare multiple parses, plus especially the ability to inspect the parsing state at an arbitrary point during the parse, are great debugging tools to understand why a given grammar is ambiguous.