(1) Extend the codomain of f and g, to N, i.e. think of them as functions N -> N instead of functions N -> {0, ..., 9}.
(2) Compute the convolution of those two functions, giving you another (still finitely supported) function h: N -> N. Usually at this point h will have values that are larger than 10.
(3) Do all the carrying (e.g. repeatedly take the first n for which h(n) > 10, and subtract 10 from h(n) and add 1 to h(n+1)). Now all the values of h are in {0, ..., 9}, so you can think of h as a function N -> {0, ..., 9}.
As I see it "therapy" is already a catch-all terms for many very different things. In my experience, sometimes "it's the relationship that heals", other times it's something else.
E.g. as I understand it, cognitive behavioral therapy up there in terms of evidence base. In my experience it's more of a "learn cognitive skills" modality than an "it's the relationship that heals" modality. (As compared with, say, psychodynamic therapy.)
For better or for worse, to me CBT feels like an approach that doesn't go particularly deep, but is in some cases effective anyway. And it's subject to some valid criticism for that: in some cases it just gives the patient more tools to bury issues more deeply; functionally patching symptoms rather than addressing an underlying issue. There's tension around this even within the world of "human" therapy.
One way or another, a lot of current therapeutic practice is an attempt to "get therapy to scale", with associated compromises. Human therapists are "good enough", not "perfect". We find approaches that tend to work, gather evidence that they work, create educational materials and train people up to produce more competent practitioners of those approaches, then throw them at the world. This process is subject to the same enshittification pressures and compromises that any attempts at scaling are. (The world of "influencer" and "life coach" nonsense even more so.)
I expect something akin to "ChatGPT therapy" to ultimately fit somewhere in this landscape. My hope is that it's somewhere between self-help books and human therapy. I do hope it doesn't completely steamroll the aspects of real therapy that are grounded in "it's the [human] relationship that heals". (And I do worry that it will.) I expect LLMs to remain a pretty poor replacement for this for a long time, even in a scenario where they are "better than human" at other cognitive tasks.
But I do think some therapy modalities (not just influencer and life coach nonsense) are a place where LLMs could fit in and make things better with "scale". Whatever it is, it won't be a drop-in replacement, I think if it goes this way we'll (have to) navigate new compromises and develop new therapy modalities for this niche that are relatively easy to "teach" to an LLM, while being effective and safe.
Personally, the main reason I think replacing human therapists with LLMs would be wildly irresponsible isn't "it's the relationship that heals", its an LLM's ability to remain grounded and e.g. "escalate" when appropriate. (Like recognizing signs of a suicidal client and behaving appropriately, e.g. pulling a human into the loop. I trust self-driving cars to drive more safely than humans, and pull over when they can't [after ~$1e11 of investment]. I have less trust for an LLM-driven therapist to "pull over" at the right time.)
To me that's a bigger sense in which "you shouldn't call it therapy" if you hot-swap an LLM in place of a human. In therapy, the person on the other end is a medical practitioner with an ethical code and responsibilities. If anything, I'm relying on them to wear that hat more than I'm relying on them to wear a "capable of human relationship" hat.