@Background Pony #B6A0  

 
There are several issues with that assessment. Firstly, Cozy’s goal wasn’t to steal all the magic in Equestria, that was just one step. Her goal was to become the so-called Empress of Friendship. The logic she uses to connect the two concepts could be generously described as spotty, but even if one were to concede that her plan could and would actually accomplish what she intends it to, it was doomed to failure the second Neighsay made his escape.
 
Further, “no advantages aside from her cleverness” is incorrect. Without Tirek’s assistance, Cozy wouldn’t have had access to the magic draining spell, the mere existence of which is extremely convenient for her. That Twilight would bring together the powerful magic artefacts she needs is also pure convenience, not to mention the tree of harmony providing a convenient hiding place for her magic circle. This isn’t even scratching the surface of how much outside her control had to go her way for her plan to go ahead at all, let alone succeed. Simply put, Cozy got lucky. Her biggest advantage, however, is her age. In a country full of suspects, she would’ve flown under the radar no matter what.
 

 
It would be more accurate to say that, for a time, she essentially had conquered Canterlot, until an event that some have called a Deus ex Machina reversed what was otherwise a perfect victory. This was only her first attempt. The second time, she successfully replaced key figures in Equestria responsible for her last defeat with changelings. Her plot was only discovered because Princess Luna alerted Starlight (discounting the events in the Crystal Empire, as we’re never shown them). Even then, the only ones who knew about her plot practically giftwrapped themselves for her in their haste to thwart her, only to be miraculously saved again, this time by an actual Deus ex Machina.
 
As for having Celestia level magical strength, this was explicitly stated to be a result of feeding on Shining Armours love.

@OtherFritz  
Cozy nearly took all of Equestria’s magic with no advantages aside from her cleverness. Chrysalis only managed to nearly conquer Canterlot (for approximately the same amount of time, maybe less) with shapeshifting powers and an army, not mentioning the fact that she apparently has blunt magical strength on par with Celestia’s. It’s reasonable to say Cozy did a better job.

So much lovely Cozy! Very nice!
 
@Background Pony #B6A0  
Did she really though?

Did a better job than you, Chrysalis.