Why not just play the melody?
Well, your audience has heard it. Sure, they like to hear it again, but that’s what the head is for. You can develop a solo off the melody. However, there are a lot of jazz players in the world; other musicians and the audience as well have heard that too.
If you follow what people in the examples did by starting with the melody and developing from there, when you go to an open jam you probably want to go straight to the fourth or fifth chorus, skipping the first few on the assumption that everyone there has already covered that ground.
However, after years of this, you start to think in terms of larger and larger musical sentences. The truth is, there are only so many classes of motifs, and eventually everything is going to remind you of some combination of things you’ve heard before. Just as a child progresses from syllables to words to clichés to forms, a longtime jazz player is interested more in when you say something than what you say, how you construct the sentence more than what words you use. OK, you played a fast scale; it might or might not be particularly impressive from a technical perspective, and it’s neither good nor bad that we’ve all heard it before; the question is, what does it mean at that point in the song, over that chord, after what you just played–and what are you going to play next that might expand its meaning?
Try it first by quoting other songs during your solos. It’s cute, but what’s the difference between a random phrase and something that makes the audience laugh?