I think there are many situations where the pattern matching depends on runtime values and therefore has a lot of overhead when it happens in an inner loop. In this cases the multiple dispatch pattern can have significant overhead.
Interestingly, after spending some time for a larger project in Rust and using its Enums+Pattern matching extensively, I had for the first time feeling that there was a feature in another programming language that Julia did not have and which I wished it had. see rust docs
However, after spending some time thinking I realized that a lot of the pattern matching convenience in Rust came from the fact that Rust is statically compiled, so the compiler could do tests if all cases were covered etc and warn you about missing cases in all the match calls in your program whenever you extended an Enum.
So in general I agree with @Tamas_Papp that I try to stick with idiomatic Julia and use parametric dispatch instead of pattern matching whenever possible. I think the main problem using one of the pattern matching libraries is that they are simply not used often enough in the Julia ecosystem to become idiomatic Julia code. So, the main goal (more readable code) is not achieved because the user looking at the code first has to get familiar with the pattern matching syntax used in that particular case. Maybe it is a circular problem, but I would use more pattern dispatch if it were more abundant in other Julia code I am reading.