Straightening as a tool, is related to the image's Crop in particular. And Crop is not so set up to sync between images, include in a preset, etc as many other adjustments are. Apparently by design, AFAICT.
If Upright had never existed, yes absolutely - Auto straightening function of crop should be a separately selectable option to include in a preset, or to sync, or copy-paste, or Autosync.
Maybe we can regard the Auto button of straighten, as a legacy survival - from the time before Upright arrived to supersede that (and to go beyond it, functionally). IMO we don't really need both options, the old type and the new type, presented side by side e.g. in presets.
We are given the ability to controllably batch apply Upright via several methods, choosing at will to transfer either the FACT of it (causing a fresh recalculation per image) or else the RESULTS of it (as have been calculated from the source image).
So far as manually defining straightening, Guided "Upright" allows drawing a specific horizon line as the Straighten tool does, but again goes beyond that functionality since multiple such lines can be drawn, and analysed together as a set.
I strongly recommend switching over to Upright rather than Straighten. At some future point, Straighten may disappear from Crop - merely speculating there.
In the past we have adapted to the loss of favourite adjustments (some will remember Fill Light) that we previously thought were essential or even unimprovable.
And we did adapt, and adopt, rapidly 1) because the replacement was soon found to be more effective and flexible; and 2) because the retention of existing adjustments on our images, was gracefully handled.
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