This would interest me. I've sometimes had trouble with the scope of choice in character creation (and in choices of action). For example, you can have the very unbounded freedom of, say, Over the Edge, where you have a bit of info about the weird setting and are told you can basically create anything, within reasonable power levels (and even unreasonable power levels, as long as you're ready for the heat). On the other, you have games like Apocalypse World, which give you playbooks with menus to choose basically all your options from, even your character name in some cases. The first can be as bewildering as it is free; the second can feel as restrictive as it is streamlining of that part of things so you can get to the action. More generally, I find that sometimes if I am thinking of how to respond or act in a situation, and the GM prods me with a suggestion or two, it shuts down whatever nascent trains of thought I had building up, and unless I have a firm idea of what I do and do not want to do, I'll default to one of the suggestions. That's a bit far afield of the OP but it seemed relevant to mention.
A middle ground is, for example, playbooks that ask specific but open-ended questions, such as the Ranger in Stonetop with its questions about "What dark threat do you see in the region?" and followons, plus the inter-character questions. I wonder what general sorts of guidelines can be discerned regarding these various approaches: What aspects of they are applied to, what is left implicit, and so on.
I'll add that playbooks with menus of options that also include blanks I can fill in are my favorite.

It makes explicit that each menu is a list of
suggestions and not a Hobson's choice.
I've read but never played Over the Edge, but you reminded me of Cthulhu Dark: PC gen in that system is very simple - choose a name and a job for your character. (Where "choose a job" is literal - you're not choosing from a list of classes or playbooks, you're answering the question for the PC the same as if, it a party, someone asked you "So what do you do?")
The first time I ran a session of Cthulhu Dark, I told the players I wanted us to play in between-the-wars Boston, they agreed, and then one said their PC was an investigative journalist, another that their PC was a longshoreman, and the third that their PC was a legal secretary. That put a bit of pressure on me as GM to think of a way to weave their paths together! I chose
the docks as the initial focus, and that worked.
The game I've played that is the most opposite of this that I can think of is Prince Valiant, where in the first session the default is that every PC is a knight: Although each player has their choice of how to allocate 7 ranks across Brawn and Presence, and 9 ranks across Arms, Riding and 12 other skills; which at least at our table produced some interesting character differences straight away.
In terms of
what general sorts of guidelines can be discerned regarding these various approaches, I'll try two initial thoughts and see what you and others think.
One is inspired by
Christopher Kubasik's Interactive Toolkit; by the remarks in the Apocalypse World rulebook about setting Hx (p 103 of my version of the rules): "the
players can and ought to bring each other into it when they’re making their choices"; and has been suggested on these boards more than once by
@chaochou: the players can work together to build their PCs, at least in general terms.
Where this takes place can be interesting. In my own practice, it often happens a bit downstream. Eg in our Prince Valiant game, three players all build their PCs separately from one another - it took about five or ten minutes at the table, as all they had to do was allocate Brawn and Presence, choose their skills, and write a brief description. Two players build remarkably similar PCs, differing only in their allocation of one or two ranks to Fellowship vs Healing. And one described his PC as "a middle-aged knight who has achieved little of note" whereas the other was (paraphrasing a bit) a young knight rather confident in his ability. We quickly decided that they were father and son; and this gave, and has continued to give, the relationship between them an interesting dynamic, a bit different from what is typical in action/adventure-oriented RPGing.
In my most recent Burning Wheel play, my friend and I agreed to each burn a PC with 4 lifepaths, and he built a weather witch while I built a bitter Dark Elf. We then discussed how it was that they came to know one another and be in one another's company. And I wrote my character a Belief that clearly connected him to my friend's character.
The second thought: I think it's reasonable to expect the GM to do some of the heavy lifting here,
and for the players to accept that. I already gave the example of
the docks. In the BW game I just mentioned, my friend and I are co-GMing (each frames the adversity for the other's PC) and we collaborated to establish the initial set-up. When I ran Wuthering Heights, each PC was generated by rolling the relevant stats and then on the Problems Table, and when one was a myopic socialist interested in the occult and the other a mute, republican, non-conformist clergyman I started with the socialist first - and established with that player that the PC worked in a radical bookshop in Soho with a more obscure upstairs section with occult texts - and then agreed with the clergyman that he had gone into the bookshop looking for copies of radical texts (of the sort the reading of which had rendered him mute!) to denounce and destroy.
I think the further upstream the players collaborate in building their PCs, establishing their connections, etc, the less the responsibility will fall on the GM and the more the players might shape their starting situation. (If this is too narrow a thought I'm interested to learn that.)