I don't want you to leave this discussion simply reinforced in preconceived notions.

Me too, so let's begin.

When we speak of "acceptance" in therapy, we're not talking about getting the patient to simply assent to their pain to a point where that pain is negated.

That is a straw-man argument, but I forgive you because I was terse. There's nothing about eternal happiness in the after-life that negates pain. The whole point is that you do feel pain, and even though it sucks now it will all be worth it in the end. Trust Me.

What we're talking about is taking a non-adversarial relationship with one's emotions.

I'm glad we can find connections between our two theoretical orientations.

Emotions evolved to aid in human survival.

Did they? All we have is circumstantial evidence. I'd agrue that the proper research to support such a conclusion hasn't been done yet, and I'd speculate that it might not be possible to do so. If you're a fan of evolutionary psychology, you might want to head over to r/theredpill.

You go on to list examples of functional explanations of emotions. One of the (perhaps intentional?) blind spots you have at this point in your argument is that you focus only on individual organism functionality. I'd argue what really matters is spieces or society level functionality or systematic functionality.

Here's what I mean by systematic functionality: the emotions one feels that could compel one to put one's self in danger in order to care for others. If individual organism funcionality is important we would expect those emotions to be rare, and discouraged by cultures throughout history. Instead, we see the opposite. If one sacrafices herself in order to save five, for example, it is a net benefit to a cultural-psycho-social-bio tradition. It would be functional for all in a traditon to have that programing in case any of them happens to (unfortunately?) find themselves in that sitution.

Continuing ...

... and the actions indicated by the emotion, are seen to be too painful, threatening, or disquieting to bear.

Maybe it's just me, but that "too ... to bear" seems too imprecicely defined. Your argument hinges on it. If one could demonstare that the emotions are bareable and problematic issues still arise, then the rest of the argument seems moot. However, if you define "too ... to bear" as anything that creates problematic issues, then you run into a tautological problem.

Here's where you really go off the deep end, IMO:

However, this person may not have the resources to cope with that threat, and thus the information contained in the fear is too threatening to be conscious of.

Note the loose definition of "resources" and "information." When you say information I think you really mean meaning (speculation on my part, for sure), and if so, I wonder if there is an alterior motive for saying that: to allow an opportunity for a therapist to redefine that meaning when the patient is experiencing an episode of shock. That would facilitate rewriting of core beliefs. Pejoritavely: brain-washing.

If I could make the reader take away one point it would be the layers of unsupported assumptions in my emphasized part of this statement:

That struggle for experiential control then takes up all their time and energy, when it would have been better spent developing the resources needed to deal with the situation the fear is about.

Claims based on hypothetical scenarios are pure nonesense. In the real world things are often not so clear cut. You may want to consider if you are enacting a cognitive distortion.

Of course, in some cases the only limitation is the patient's attitude. For example, consider an attractive young woman who only need not be shy to recieve attention from men.

Many patients suffer from problems that have a material interpersonal components, and the interpersonal aspect, in my view, introduces complexities that make it nearly impossible to make justifiable claims about what "would have been better" (a clever rhetoric trick to say what the patient "should" do when you have enough self awareness to think that saying "should" would make your argument less persuasive).

Even if you had perfect information about the patient's experience, you would not have access to the internal world of the others the patient interacts with. Theory can help with this problem but the value gained is still limited, at least asmptotically.

A person's life can fall apart when they spend their days fighting their emotions, but neglecting the situation those emotions are about.

OK, I'm sure there are people who could be accurately described that way, but without specifying how one would know if one's behavior "fighting their emotions" versus taking the most reasonable actions given the available information, the utility of your conception of "acceptance" has limited value. Maybe you weren't aiming to be so thorough, and criticism like that could be addressed by citing more thorough sources; if so I don't think we're in dissagreement.

For instance, the case of grief.

I can't help but notice the carefully chosen example that has important features that make it different from other (perhaps more common) problems. I covered some of this above regarding interpersonal problems.

However, grief still evolved to serve an adaptive purpose: ...

Here, again, you focus on the individual organism functionality without considering the systemic functionality.

Here's an alternative (though I'm not claiming it is actually true) theory of grief: grief allows a society to decide if it should cut dead weight or increase attachment to more periphrial parts of the network.

Members of a society contribute and consume resources. Resources are negotiated through social networks, with nodes connected by (perhaps among other factors) attachment. To the extent you are attached to someone you experience more grief in response to their death. The interaction between drives to connect and to issolate are functional to the survival of the dominant culture and the subculture that the deceased individual connected (negotiation, resource transfer, and accounting of resource transactions). One can imagine scenarios where connectedness and disconnectedness could both be functional, depending on the circumstances and the perspective of the dominant or subcultures.

If there's a second take-away point, it would be the loaded term I emphasize in this next quotation:

If we try to shut down the grief ...

Who decides what is and what is not a "shut down" reaction? Apparently, the therapist. This is similar to the definition of "accepting relationship": how convenient that the therapist gets to decide what is or is not an accepting relationship versus "shut down."

Finally, I want to highlight an issue that is brought to the surface due to the use of grief as an example (emphasis mine):

... simply because the situation it's about is very painful and can't be changed

A component missing (understandably, given that you're following up on an example of a loved one's death) is the time horizon dimension. It is easy to dissmiss in (the probably more common) case where the loss is issolated to a particular point in time, but when the loss is chronic (e.g. chronic issolation, rejection, discrimination, or predudice) the time dimention becomes more salient.

What exactly are the functional aspects of on-going grief related to a (relatively) unchangeable chronic condition, where the loss is experience day by day, drip by drip? What exactly is gained through abandoning experiential control when control behaviors are directed to (ultimately futile) efforts to develope resources needed to deal with the situation the fear is about?

When nearly contradictory strategies rely on the bifurcation of controlable versus non-controlable problems, how is one to proceed when all that can be determined from a situation is that it has not yet been shown to be sensitive to influence by the patient?

If a material "healing" component is the sense of mastery one's feels when thinks one is "developing the resources needed to deal with the situation the fear is about," perhaps we should decieve those who are probably completely hopeless so that they can achieve at least a quantum of solace.