ARC languages are Turing complete, but some algorithms require more than just "peppering weakrefs" and actually require you to essentially build your own GC.
Consider a graph which can have nodes added, and edges added or removed. Say you want to keep track of the part of the graph that is connected to a node.
You can't know ahead of time which references can be weak. So all must be strong and you will leak memory when a circular part of the graph becomes disconnected.
In general, garbage collection is a difficult problem that solves a lot. You can't trivially do without it. It's not just a tool of laziness.
ARC won't work when you cannot determine ahead of time where the cycle can end safely. Pretty sure for an interesting set of algorithms this is a problem.
It's something I find annoying about some ARC/Rust enthusiasts: their belief that because they haven't found need for a GC, that there isn't one.