Here's my take on each of the points you raise:
Unfriendly community, questions are received with down-votes
I know many people feel this way but my experience in the SE network has been the exact opposite. Downvotes are not bad. Let me repeat that. Downvotes are not bad. They are in fact precisely what makes the SE sites so useful. We need bad posts to be downvoted, that's the only way good posts come to the top. yes, some people can take the downvotes as an insult instead of as an invitation to improve their answer. Quite simply, those people won't have a good time here so it would be better for them—and us—if they go to another site.That's not a problem, there's enough to go around.
That really isn't my impression of SE and I feel that most people who feel it's toxic simply don't understand the system and consider downvotes and closed questions to be personal attacks. With the possible exception of SO which is orders of magnitude larger than any other site, most SE sites are relatively friendly as long as you put some effort into your posts. Yes, dumping your homework with no attempt to solve it and asking others to do your work for you are not well received. Well, they shouldn't be.
However, I have been quite active (>10 or 20k rep) on 4 sites of the network, I'm an elected mod on two and participate in quite a few more. I haven't felt any of them were in any way "toxic". Maybe I was lucky, granted, but I really think the "toxicity" is almost entirely born of simple misunderstandings about what the SE site are and are not.
Lack of support from moderators
I don't really know what that is supposed to mean. I see some complaints about too much moderation in the linked biostars post but none of a lack thereof. Also, most people who're not familiar with SE tend to assume that anyone who cotes to close a post or edits or does anything else that wouldn't be possible by users on traditional forums is a mod.
Lack of discussion about questions
Yes, absolutely! SE is not a forum and not the right place for disussion. But that's great! If you need a discussion, you can always go to Biostars or SeqAnswers or even our chat. This isn't a place for discussion, it's a Q&A site. That's fine: to each their own.
Adding more sites is diluting the user base
Dunno about that. I, for example, find both SeqAnswers and Biostars unpleasant, chaotic and far harder to extract useful information out of than the SE sites. Which is why I am so pleased with this proposal. So it's not so much a question of diluting the community as it is one of offering multiple venues where each of us can find their niche and the site they find most useful. There are enough bioinformaticians around by now that the community can support multiple sites, I think.
Cross-post with other communities
Why does this matter? If another community has a useful piece of information, we copy it over. That's the beauty of open licenses.
License of the code provided in Stack Exchange
Again, for me that's a feature and not a bug. Any code posted here can be used by anyone else in the community with attribution. Surely that's a good thing?
In summary, there's no reason to please everyone. This is an SE site and the SE network has clearly demonstrated that there are many, many users who enjoy their system and find it useful in their work. Other people find it too restrictive or negative or hard to deal with. That's absolutely fine. Those of us who like the SE system are free to use this site and those of us who don't are free to use the others. Nobody is forcing anyone to do anything.
So yes, we should be friendly and open and helpful to newbies. Ignorance is never a sin. On the other hand, laziness and unwillingness to put effort into your question and answer are, and I see no reason why we shouldn't have strict quality standards. Many SE sites cater to both experts and novices and the level of expertise is far less important than the effort put into a post. So as long as you don't use this site as a substitute for doing your own work, you should be welcome to ask a question of any level of expertise here. But not things that would be answered by pasting the question title into Google or Wikipedia. Some effort is required, yes.