Alternatively, burning down Teldrassil was tactically necessary, if only to prevent the Night Elves from ever trying to come and take it back and resume the Azerite shipments.
Not exactly. It was explained that Sylvanas didn't want to destroy the Night Elves, as it would just embolden the Alliance to counter attack. She wanted to occupy Teldrassil, because then she could use all the civilian survivors as hostages, hoping the death of Malfurion would make them scared and docile. The Alliance wouldn't attack the tree, since it would be very fortified by the Horde, and they wouldn't have a decent staging ground outside of Azuremyst, considering it's implied the Horde has mostly taken Kalimdor by this point. By destroying Teldrassil instead, she removed her ability to use them as a political barrier, unable to threaten their executions should the Alliance invade. It was a much worst tactical situation, and is what leads to her losing the Undercity to the Alliance.
The Humans have stopped at nothing to recover Lordaeron from the Forsaken, even though the Forsaken in this case ARE the former citizens and lords of Lordaeron and -they- were the ones to recover it from the Scourge in the first place, but suddenly it's okay for the Alliance to commit genocide against the Forsaken to recover a capital they haven't set foot in for damn near 20 years? Sylvanas probably didn't want another god damn lifetime of people trying to take the city back, especially people she actually sees as threat
You do realize the Scarlet Crusade isn't the Alliance, right? The Alliance has mostly abandoned the northern lands outside of Gilneas, and an attempt to rebuild Andorhal which didn't really work out. The rest is run by neutral parties and the Forsaken. The Scarlet Crusade was the only antagonistic outlier and they were wiped out by both the Horde and Alliance.
Also, my guess is you didn't read the latest novel, which actually went into detail about the
diplomacy being attempted by the Humans and the Forsaken, with the governing body of Undercity (The Desolate Council, put into place while Sylvanas was leading from Orgrimmar) even going so far as setting up of a meeting between both living and dead family members. It was going so well that Sylvanas ended up executing the Desolate Council and then the citizens that went to the gathering, as she worried giving them hope of a life with their living family again would turn them against her (the fact Calia Menethil showed up again didn't help). She spared the living people though, purely so Anduin wouldn't prematurely start the war before she had a chance to scheme and make the first move.
Only now after the burning of Teldrassil, has Anduin decided to invade the Undercity as retaliation.