Wheel of Time

First, burning out comes from channeling more than your body can handle, NOT more than your soul can handle. Related, the rules of Wheel of Time place no limit on how much power any trained channeler can draw. They just burn themselves to death instantly without being able to use it... Or ride the line and do one last blaze 10x or more stronger than they can safely handle. "Weep For Manetheren".

Pointing to the above, the important point is that an untrained/unseasoned Rand canonically could not channel as much power as Aginor can. Aginor is formally rated ++2 in the power, with Rand ++1, but the difference between "initial strength" and "potential strength" is at least 2 full tiers at those power levels... making baby Rand likely a full tier WEAKER than Aginor at the Eye... Whether it came from an untainted pool or from himself, it would have killed him as easily as if they overchanneled himself. And Aginor "burned himself to death instantly" drawing/doing less with the Power than Rand does. For the above reasons, he also has no real motivation to have drawn all that power. Canonically perhaps the most analytical/scientific-minded of the Forsaken killed in a mad power grab he didn't even need?

Second, there is an important difference between a Pool of Saidin and an angreal or sa'angreal. The latter generally do two things - they increase how much of the power you can draw without injuring yourself, and they provide what is referred to as "a buffer" that physically prevents you from overchanneling. So as unpleasant(and addictive) as can be, you are safe going balls-to-the-wall with twice your naked potential when you hold an angreal.

A pool of saidin having no enhancing or buffer effects, Rand channeling something he could easily do with an angreal should still kill him. And what he does at the Eye is pushing it compared to things he does with sa'angreal.