Here's a question: Why did Thomas nominate Longstreet for Secretary of War in the first place?
(Close distinction: I buy your argument on why he would be appointed if he was nominated, my concern is the initial nomination)
Appointing anyone from a former CSA state is questionable. Whether rational or not, the public would be greatly concerned regarding their loyalty, there could be a great backlash.
Admittedly, Thomas greatly disliked establishment politicians and their concerns. But in that case why would he care about party lines either - taking a pure ATL viewpoint and not a for-the-sake-of-your-TL viewpoint, he would be more likely to appoint Grant as Secretary of War. He knows the man and that he is a good commander, and not necessarily the best in civilian life, and not very partisan either. All good reasons, plus the whole breaching-party-lines thing; and remember Grant comes from Illinois. Regionally balancing the cabinet was a very big deal at the time (see Team of Rivals for details). Could be a cool spin-off TL......
Or failing that, why not any other of the half-dozen or so good commanders Thomas served with during the war?
Or - assuming that we have established that Thomas wants to appoint someone from the former CSA - still, why Longstreet? He was well-known but not in the highest command echelons, and had little-to-no political experience - plus Thomas only briefly faced him during the war, and would have little personal knowledge of him.
It seems to be he would be more likely to appoint someone like J. Johnston - army commander, pretty much universally liked (except for Davis), had some personal interactions with plus knew him as a skilled opponent.
Or - here's some fun - Robert E. Lee. The two of them were old 2nd Cavalry buddies, Thomas knew his character quite well. Frankly everyone in military circles, on both sides, had nothing bad to say about his character. Lee had administrative experience from serving at West Point. Plus he was darn infamous in the north as "the man who made the war last for 4 years", so Thomas can point out: "if he could do all that while leading half-starved and poorly supplied men during the war, imagine how well he can direct a properly equipped army like ours".
That could be another fun spin-off TL. Of course, I'm a sucker for anything with an interesting professional relationship between Thomas and Lee.