Actually, one big reason a woman might feel a bit 'confused' about getting into a FWB set up is because of the endless fucking propaganda that women want and need 'love' more than sex. It is not compulsory to have a longterm, sexually exclusive relationship. Not everyone wants one.
I agree with SGB here. However, I think that you have to be very very sure that deep down that is what you want. Because if you aren't sure, or you're feeling vulnerable for any particular reason, FWB relationships are a very good way to end up feeling really appallingly bad.
The OP has already identified that she is still working through issues from the previous relationship, and that she is interested in the optential-FWB as a human being, rather than as a shag (i.e. she is in a position where deeper feelings are fairly easy to develop, whether or not this is part of the plan).
I wrote about FWB on a different thread a couple of days ago, where someone was asking what's wrong with someone having lots of sexual partners. Basically I was trying to use a FWB situation to prove my own inner strength (predicated on my appearance and my sexual prowess - hardly good things on which to be basing inner strength). Unsurprisingly it didn't work. It took me a while to work out what was wrong, and I should have stepped back and understood my own motivations better before ever getting into that situation.
"But with respect to the "what's the problem" bit, is it possible to voluntarily have no-strings-attached sex with lots of different people, without doing a pathological level of dissociation? Sex is - at least in theory - fun and pleasurable, but it is also a rather intense level of intimacy with someone, and -when done correctly - it releases all sorts of bonding hormones (oxytocin). Repeatedly lying next to a new partner bathed in an afterglow of oxytocin, and then getting up and never seeing the person again - and then doing the same thing a week later with a new partner - either requires you to blunt the reponse to all that intimacy and oxytocin - or it leaves you in a bit of a mess if you're responding to it and then sublimating the response in order to get it on with the next person.
Aged 27-29 I tried to be terribly sexy and grown-up and have a "fling" with a philandering twit who praised my beauty and sexual prowess to the skies, while making it very clear that the relationship wasn't ever going to go further than dinner, banter and sex. I felt very grown-up that I could so totally handle it, that I wasn't needy, that I was utterly autonomous. After the initial self-importance had worn off, I ended up a total blubbering mess after every session. Not in front of him - crying by myself for hours, unable to understand the intensity of the unhappiness. I couldn't handle blunting the response to the intimacy - and frankly it was idiotic of me to try. I look back and think he was abusive and strangely blunted in his own emotional responses.
That's why no-strings-attached sex is extremely hard to achieve - and why it hardly seems worth achieving. It hurts so many people, so badly. Why bother?"