My view on relationships is it's entirely based on compatibility between you and your partner, that sounds obvious but it does reflect certain consequences here.
So if relationship is entirely based on compatibility, than someone could indeed go into a relationship straight away without going through friends and so forth as Grovy says, and they may still have a very happy and healthy relationship. As long as the two people are compatible, the relationship will work.
However, figuring out whether someone is compatible or not is quite tricky! Most people act differently in public than they do in private, so when you meet someone first off, you may only think their public side is compatible, while their private more secretive side may not be. As well, you and your partner will change over time, which means that if you were compatible at one stage you may not be compatible at a different stage, this is why it's very rare for a relationship to go on and remain healthy and exciting for a long time (while most relationships last a long time, not all of those are happy and healthy).
So going through the friend to partner stage is generally a safer way to get a long-lasting relationship, but there are still chances that the relationship can fail cause you may change, and meeting someone randomly generally won't work out as often because you don't know of someones compatibility, but it can still work out if you're lucky. There's a whole slew of other things that need to be taken into account including how desperate someone is and other internal biases.