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human
[ASOIAF] Would the Targaryens ever have conquered Westeros if the Doom never happened? Would they have risked attracting the attention of other Dragonlords? What would a Targaryen ruled Westeros have been like in a world where the Valyrian Freehold still existed?

I know the Targaryens arrived on Dragonstone before the Doom, but they only attempted to conquer the Westeros after Valyria fell. Was the Doom a major reason why the decided to go through with it, or would they have made their bid for the throne even if Valyria had still been around to 'see' them taking over an entire continent?
gpt
The Targaryens were among Valyria's dragonlords, a middling at best family of Valyria's dragonlords but still among the top strata of Valyrian society. If they'd had conquered Westeros then Westeros would likely have had an influx of Vaylrian and other Esterosi migrants colonising it, and the Targaryen's would have earned significant prestige among the Targaryen nobility along with significant wealth and power to make them among the greatest of the Valyrian lords. 

As that would be the outcome of a successful Targaryen invasion it's quite possible other Valyrian nobles would had tried to impede Targaryen preparations for the invasion but being in Dragonstone, the farthest flung rock of the Freehold comes a certain isolation from an opponent's spy networks which would hinder any rivals attempts to do so. 

It's possible the Freehold didn't allow individuals to organise and carry out military action independent of specific authorisation from Valyria in which case the Targaryens might not have been able to carry out the invasion at all or would have faced severe penalties for carrying out an invasion, however that's just speculation.

> Was the Doom a major reason why the decided to go through with it 

No, there was over a century between the Doom and the start of Aegon's Conquest. Aegon was taking advantage of the opportunity Harren the Black's actions in Westeros had opened up to make himself a major player rather than a tool for the Free Cities to use as his family had been to some extent during the preceding century (the Century of Blood).

> or would they have made their bid for the throne even if Valyria had  still been around to 'see' them taking over an entire continent? 

It's possible they'd still go with it although they wouldn't have been the Kings of Westeros afterwards, the Freehold didn't have kings. Westeros would have become a collection of new provinces in the Freehold.