PS and AI are two different software created by two different engineers teams.
Wonder why this is bothering you.
Is there a good reason for this?
Of course. I don't know about Illustrator, but with Photoshop, the various modifier key / handle combinations all have different functions. You can scale while maintaining aspect ratio with the corner key, and scale symmetrically by adding the Alt key. Shift dragging a mid point handle scales just width or height, but keeps things nice and square (prevents skew). That is immensely useful.
There are too many options to list them all, but go try Free Transforming a square object via its corner and mid handles and try all combinations of Shift Alt Ctrl (Shift Opt Cmd).
In Illustrator, I can do this by holding the shift key while click+dragging.
Not in my version of illustrator. ( Illustrator CC 2015.3 ). It work as in PS.
Shift dragging a mid point handle scales just width or height
I see no difference between shift+dragging a midpoint and simply dragging a midpoint. Do you?
Shift+drag should mean proportional scaling regardless of anchor point.
Upgrade your software, bruh.
2017 lets me shift+drag any anchor point to scale proportionally.