This just doesnt seem right...

No, it doesn't. Welcome to Illustrator.

• Note that Gradient Swatches cannot be set to Global.
• Note that each application of a given Gradient Swatch can have its own angle and spread. The angle and spread are not stored in the Swatch, but with each object.
• Note that the Swatch Options dialog for a Gradient Swatch does not provide any Gradient editing. It's the same dialog as for ordinary solid Swatches, and everything is grayed out.

So you can use the eyedropper to copy a Grad fill, including its angle/spread, from one object to another. But you can't update a Gradient Swatch by AltDragging the object onto the Swatch, nor by AltDragging the object's Fill from the Appearance Palette onto the Swatch, but only by AltDragging the Swatch from the Color palette (where, by the way, it doesn't even belong; a Gradient is not a color) or from the Gradient palette, but in those cases the angle/spread is not stored.

You can, however, drag an object containing a Gradient into the Graphic Styles palette. Then you can apply that Graphic Style, including its angle/spread to other objects. Then you can edit the Grad stops, angle, or spread of one of those objects and AltDrag that object onto the stored Graphic Style, and other objects with that Style applied will update accordingly.

Doing that, however, stores/updates all of the modified object's Appearances in the Style. So if the modified path also has a Stroke, AltDragging the modified object also causes the Stroke to be added to all other objects with that Style applied.

1. You can workaround that  by applying the Gradient at a Group level, rather than at the object level, storing that as a Style, and only applying it to other Groups. That requires some careful planning. For example:
2. Draw three unfilled paths, each with a different Stroke.
3. Select each one individually and Group it, so you have three Groups, each containing one path.
4. Select one Group. Apply a Grad Fill to it.
5. Drag it to the Graphic Styles palette.
6. Select the other two Groups. Apply the Style.
7. WhitePointer: Select just the path inside one of the Groups. Give it a thick Stroke. Deselect.
8. Select the same Group. Gradient palette: alter the Grad.
9. AltDrag the modified Group and drop it onto the Style. The Grads of the other Groups update, but their (object-level) strokes are not wrecked.

Of course all that requires an awful lot of foresight and pre-planning.

• Note that Illustrator is exceedingly confused, scattered, inconsistent, and utterly unintuitive.

JET

You may want to use the Merge Swatches command.

1. Set up your new gradient fill and define it as a new swatch (g2).

2. In the Swatches palette, first select g2, then (Cmd) select the swatch you're going to replace. Both swatches are highlighted now. Note that the order of selecting the swatches is important.

3. In the Swatches palette flyout menu, execute the Merge Swatches command.