It appears that keyblades do not spontaneously generate from hearts.
The only Keyblade we really know how it 'spontaneously generated' was Sora's, and it does seem that it kind of spontaneously generated. After all, Riku's had it for years, but it never did him any good, but the instant Sora reached for it, poof, it's there.
Until we know more about at least Mickey and Riku's Keyblades, it can go either way. I'm leaning more towards it yes popping up at random.
It has been speculated that the appearance is based on the heart of the weilder, but this does not seem to be the case. The keyblade Sora uses was around before he ever used it. It cannot, then, be his reflective weapon.
Only it is.
Mickey's Star Seeker is a reflection of his time with Yen Sid.
Riku's Way to Dawn is a reflection of everything he's been through.
Every single Key
chain Sora got after the KK is a reflection of what he's been through and the people he met.
The KK and IKK seem to have a unique, irregular origin that's linked to BBS, probably. It's not to be used to generalize over the rest of the Keyblades/chains.
Also, Riku's Keyblade was there before he found it. Also, keyblades can retain their shape when the user is gone.
The only Keyblades we've seen that retain their shapes without the user are ones without Keychains.
Leaving aside the plethora of Keychainless Keyblade we see in the KH2 secret endings due to questionable canonity, we're left with Aqua's Keyblade seen in the room of sleep - but we cannot say without a doubt that Aqua's really gone due to the unique and thus far unknown nature of the room, or if that's even really her Keyblade and not part of an illusion Xemnas created for himself in an attempt to maybe reach his lost Memories.
Nice insight, but it's either wrong or too unbased it's too easy to say otherwise.