Indeed I did not follow what you meant. I missed the "persistent" and saw ... "don't incur the cost of copying." I took that to mean that you were referring to not maintaining any history and using a single, mutable global state. It is with that understanding that I made the previous comment.
To address what you meant ... it's more a matter of what's practical. For example, to parse C++ one needs to do quite a bit of semantic analysis during parsing. A full implementation of the type system is necessary. Then the data structures change with every statement/clause parsed. Achieving this with persistent data structures is far too costly.
