"Going down the rathole" vs. "Going down the rabbit hole."

I hear/read the phrase "going down a/the rathole" used as a synonym for the phrase "going down a/the rabbit hole," the later taken from chapter 1 – "Down the Rabbit Hole" of Alice’s Adventures in Wonderland, by Lewis Carroll.

For example, "let’s not go down a rat hole," "that topic is a rathole," etc. I’ve often encountered this in meetings where a topic or past event is brought up and is then responded to with "let’s not go down that rat hole," or a similar variation used to state that a topic, or issue is so confusing, complex, or outside of reality and reason that it would be impossible or at least not beneficial to discuss. There could a time component, but the main point is being unable to reason about something.

Google’s definition of rathole is

noun: rathole; plural noun: ratholes; noun: rat-hole; plural noun:
rat-holes

1. informal a cramped or squalid room or building.
2. NORTH AMERICAN informal used to refer to the waste of money or resources. "pouring our assets down the rathole of military
   expenditure"

One of Wikipedia’s explanations of rabbit hole is

"down the rabbit hole", a metaphor for an entry into the unknown, the
disorientating or the mentally deranging, from its use in Alice’s
Adventures in Wonderland a slang expression for a psychedelic
experience, from the same usage.

I cringe when I hear rathole used instead of rabbit hole, because of two issues:

1. What exactly is a rat hole (is this really a widely known fact or idea)?
2. The deeper idea (e.g. magnitude of the confusion) trying to be conveyed seems to be lost with rathole because the reference to Alice’s Adventures in Wonderland is at worst lost, or at best greatly degraded. Consider vanity versus narcissism — the later having a mythological aspect which communicates a larger idea in a single word.

My question is this, are both usages correct/synonymous to state that discussing an issue or past experience would be so disorienting, complex, or confusing, so as to not be beneficial?