I have to disagree here.
The way I see it, relationships should be developed in levels. First on the platonic. Get to know the other person. Form a close bond before you decide to make the very serious commitment of a romantic relationship.
Then if you do think it's worth taking that next step, go for it. But if it doesn't work, that shouldn't discredit everything that's been done before. Friends and partners are two very different kinds of bonds with different implications and responsibilities. Just because a romantic connection doesn't work, does not mean a platonic connection won't either.
I myself have been making an effort to reconnect with my ex after I found some stuff out. I felt really bad for the way I had been villianizing her all this time, because I found out a lot of the stuff I was mad at her about likely weren't true. So I reached out to her again, and over the past couple months I've enjoyed getting to talk to her again. We don't talk often, but when we do it's nice. And I can tell she appreciates the effort because she also makes the effort to start a conversation every now and again.
If you break up with someone, don't cut them out of your life. Of course a lot of this depends on context and the circumstances around the breakup, but the idea that one just shouldn't try to be friends with an ex partner just doesn't seem right to me.