Y'shtola's actions at the House of the Crooked Coin did not cause the depleted aether in Othard or Eorzia. Y'shtola specifically brings up crystals loosing their aetheric charge before she and Hein even go to the Steppe.

Manipulating aether at the House of the Crooked Coin has a long and storied history. Y'shtola is simply the last person to manipulate the aether there and she's probably the most benevolent person to do it. Both in motive and in effect.

The first time aether is manipulated at the House of the Crooked Coin is all the way back in the 3rd Astral Era. Someone (and we have enough information to make a good guess of who it was; it's probably Amon or an Allagan scientist working with him) uses the crystal to stop the flow of all aether to the Burn. This makes the land lifeless and perfect for hacking off pieces of it and floating it using the crystal's aether. This happens sometime before the Allagan war with Mercydia ends as the lore book makes mention of experiments developed in Azys Lla being used in that war. Most importantly, the flow of aether of aether to the Burn is never restored.

The second time, the crystal is used to get Dalamud into orbit. Again, it's probably Amon (or people working with him) who does this. This is after the war with Mercydia. And still the aether to the Burn isn't restored.

After this, five thousand years and three Calamities go by. This entire time, the Burn has gone without aether. During this time, Solus comes across it and says this is what happens when too many primals get summoned. Yeah right.

The third (and probably last) time aether is manipulated at the House of the Crooked Coin is by Y'shtola. And it's specifically to restore the flow of aether to the Burn. She's finally fixing an imbalance in the world's aether that has been around for 5,000 years.