Partially true.
The only High Elves who were kicked out of their home, was those who ended up residing in Quel’Lithien.
They were kicked out following the retaking of Eversong Woods when Rommath and other magisters returned from Outland, and taught the Blood Elves how to siphon magic from living beings - which then brought them enough strength to finally kicked the scourge remnant back, at large and retake Eversong Woods and rebuild half of Silvermoon City.
The Quel’Lithien High Elves did object to the siphoning magic of living beings, and Lor’themar decided that he could not risk insurgence in Quel’Thalas at such crucial time and decided to kicked them out rather than risk infighting later.
High Elves of the Kirin’tor and later The Silver Covenant, Quel’Danil, Theramore and other Alliance cities never chose to return home to aid their people. A minority in the Kirin’tor may have returned with Kael’thas after the scourge invasion, but many did not, and they chose the Alliance over their own people at that moment.
Also, you just turned Jaina and the Silver Covenant into villains for kicking Blood Elves out of Dalaran.
No, they send spies, saboteurs and invaders.
Let us get real here, this was just Sylvanas using the situation for her own gain. The forsaken was still largely needed to protect Ghostlands, Rommath adviced Lor’themar to just relinguish Ghostlands for now, but Lor’themar refused to do that and bend the knee to Sylvanas.
It had nothing to do with Garrosh or Thrall.
Sylvanas prioritized.