A crutch is nothing more or less than a support. Perjorative doesn't necessarily apply.
Appeared as far back as 900 in old English. Many uses. A few quotes from the OED-
Crutch- c. a prop, a support.
1602 Your favour will give crutches to our faults.
1772 The hunters fix their crutches in the ground
17th c. A forked rest for the foot in a side saddle.
1861 Old crippled buildings, propped up with posts and logs.
1682 (Dryden) Two fools that crutch their feeble sense on verse.
1890 This feeble government, crutched.....


crutch as a verb in print in 1681.

What is a "real" crutch"? Modern equivalents of the staff are the "walker," the stick with four terminations, the frame with four terminations, etc.

I will admit that the image first to mind is a forked stick.