What prohibits from burning an Edge you don't control?

I would say, the same thing prevent you from burning an edge you don't control that prevent you from burning pool you don't own.

Ankha wrote:

I can't find any rule reference for that matter.

Name: Lucinde, Alastor
Camarilla Ventrue Justicar: Lucinde can enter combat with any ready non-Camarilla vampire controlled by another Methuselah as a action. During your untap phase, you can burn the Edge to give Lucinde 1 blood from the blood bank.

I can't find it either.

"Burn the Edge" effects are only usable if you control the Edge (unless otherwise specified).

This applies to: 419 Operation, Alonzo Guillen, Deploy the Hand, Emily Carson, Eric Kressida, Extorsion, Hartmut Stover, High Priestess Angra Mainyu, Isouda de Blaise, Lady Constancia, Leverage, Lucinde, Alastor, Mapatano Utando, Powerbase: Zürich, Sabbat Threat, Sarrasine, Shatter the Gate, Soldat, Torvus Bloodbeard, Tragic Love Affair, Victoria and Victorine Lafourcade.

1.2.3 defines how one obtains the edge.

And 1.1.2 & 6.3.3 define "burning the edge" as you must have the edge to burn it.

It's not about the edge, it is about paying costs. One could imagine a card like that:

Reset
+1 stealth action.
Burn the edge.

That would burn the edge no matter where it is on the table. (Please don't print that, we have enough crappy cards with the edge already )

But IIRC there is currently no such effect. All effects that require edge burning do so as a cost ("burn the edge to..."). The general rule should be: you can only pay a cost with resources you own/control.

The analogy with pool is: your actions can burn someone else's pool, but the cost must be paid from your pool.

Well, there's always Edge Vitiation:

Name: Edge Vitiation
Cardtype: Action
Cost: 1 blood
Discipline: Serpentis
+1 stealth action.
[ser] Only usable if your prey controls the Edge. Your prey burns 1 pool and burns the Edge.
[SER] Put this card in play. Whenever your predator successfully bleeds you, you get the Edge instead of your predator. Any minion can burn this card as a action.

But this one does read "Only usable if your prey controls the Edge."