DAG-enforcement versus garbage-collection?

Working on a new version of CapFs (that I'm considering a rename for to
RumpelstilskinFs), I come to the act of deleting files.

In the old CapFs, there was a real distinction between files created in
the main tree structures, and symbolic links. In the upcoming version this
distinction becomes less clear, making some kind of reference counted
delete a potential alternative to soft-link-braking deletes.

This in turn however raises an interesting pseudo-philosophical design
question. A question that I think I can best pose in the form of an
hypothesis :

"The principle of least authority and cyclic references are mutually
exclusive"

If I assume that this hypothesis is true, than the option of introducing a
DAG-violation error when a file-system user tries to create a link that
would violate the directed-acyclic-graph structure of the file-system
would likely be a much better option than one that uses garbage collection
algorithms.

With my limited imagination I've not been able to come up with a scenario
where a DAG structure either wasn' t possible or did not improve the POLA
properties of the cyclic-reference alternative, at least for the
file-system scenario, and given that any GC solution I've found greatly
degraded the least-authority aspect, by giving the collector an abundance
of authority, I'm inclined to take the above hypothesis as an axiom.

If we zoom out a bit from the specific file-system scenario, I would be
very interested to learn if anyone knows of any example that would proof
this hypothesis false. And if this hypothesis can indeed be proofed false
with such an example, I would still be interested in learning if a system
that strictly enforces the DAG structure of permission graphs would be
prohibitively restrictive for the creation of least-authority based system
designs. That is, are there examples where a DAG based alternative to a
cyclic graph would either not be possible, will yield worse adherence to
POLA, or would be restrictively more inconvenient than the cyclic
alternative.

For CapFs, a GC algorithm currently seems like a really bad fit, but DAG
enforcement would be relatively easy to fit in combined with basic
reference counted deletes. If DAG-enforcement would generally be a good
POLA concept, it would be a really interesting addition.