TL;DR - I believe that the expertise in biophysical techniques and biology is low over here and many times biophysics questions are closed due to being too biological. Therefore, another SE website might be needed to fix these issues.
What is Biophysics?
Biophysics is defined as the "the science of the application of the laws of physics to biological phenomena." As you can see, biophysics is mainly a subtopic of physics.
Biophysics have many of its own techniques and methods for analyzing biological systems. Some of these methods may be applied to a broader class of physical systems but still, the expertise on these topics is very low. Being in the field of biophysics (doing a research project in quantum biology), I myself have experienced this. My interest is in the environment assisred quantum transport of excitons. Recently I was researching on Forster Resonance Energy Transfer, a theory describing how the excitons are transferred in certain conditions. I have asked a few questions on that over here. For example This question was orginally asked on Physics.SE but got no responses. Similarly, this one also got no responses on Physics.SE. If there were a biophysics.SE I believe that it would be more specific to biophysical techniques and that it would bd much easier to find people with the expertise in the field. Therefore, questions like mine, although are purely physics questions, have a better chance of being answered if there is a successful Biophysics.SE website.
Now, let me simply analyze some of the questions under the biophysics tag. The first question is about the eye. This question is mainly physics, but some biology knowledge is needed to understand and answer the question. It seems that not many (active) people in the community have that kind of knowledge or otherwise it would have been answered.
Here is a question I do realize is a little bit on the bad question side but even with research, let's say the question is adapted to more like
Why can't rod receptors only allow us to visualize grey and black at night? What necessary physical factors about the rod receptors would be needed so we could see color at night?
Based on the reasoning seen in the comments, it seems that it still would be closed as off topic since "it is about eyes, not physics". On the other hand, if there is a Biophysics.SE site, this question would be definitely on-topic and would make a great question.
Another question is about why do ears pop?. In the comments, there are five people agreeing that this is off-topic because it is about human physiology. Them there are another five people agreeing that this is on-topic (the 6th upvote is by me). This seems to be very debatable. However, with a Biophysics.SE site, we can have such great questions being perfectly on-topic!
Now let me analyze some of the questions on the Biophysics.SE website. Let me start with this one. Certainly, this is a physics question, but you need to know the operation of the dorsal closure of fruit flies. Does anybody here know about that? I don't think so (I do admit I do not know either, but that is irrelevant). Plus. I think many would agree that this requires too much knowledge about a biological process for it to be on-topic on Physics.SE
This question also would have a problem with needing too much biology knowledge about ATP and concentration gradients and molecular motor. I believe that this would also be closed on Physics.SE as well.
After doing an analysis by sampling questions and including my own experience, here are the main points that support the forking of the biophysics community:
There is not much expertise in the biophysical techniques in the Physics.SE community
There can be too much biological knowledge needed to answer a question, even though it may be mainly physics-based
Many times the questions will be closed because it is too biological and does not ask much about physics.