The ability to save an appearance of a selected object.
The ability to save an appearance of a selected object to apply to other objects. Much like the copy and paste layer style in Photoshop.
You can do that by using Graphic Styles panel: https://helpx.adobe.com/illustrator/using/graphic-styles.html
THank you Margaet, that helped immensely! Although having the ability to use the eye dropper for a quick apply would be quite handy and would help make the experience from illustrator to indesign more consistent.
Margaret Trauth commented
This already exists. Open the Graphic Styles palette and explore.