This is not necessarily true. It depends on a language, e.g. Go is slow, Nim[0] is extremely fast with conventional GC and slightly faster with ARC/ORC[1].
GC programs can be faster than manually managed ones in some cases. It's just manual memory management gives you more control of where and when free is called. And a good type system is a privelege that gives Nim more control with destructors.
Another scarecrow of safe languages is GC pauses, which is also not a thing in Nim, see table in [2].
[0] - https://nim-lang.org/
[1] - https://nim-lang.org/blog/2020/10/15/introduction-to-arc-orc...