We should definitely allow hand-drawn schematic. I'll prefer a tidy hand-drawn one over a chaotic Altium one every day.
Now, we should also be pretty selective on the quality of illustrations we "welcome". Just as when in written text, the lack of sentence structure and punctuation, or abuse of terminology, will make a question ambiguous or unintelligible, a complex badly drawn schematic is a non-starter. Simple as that – the means of representation must suffice for the question asked.
The drawing of a complete discrete four-stage audio amplifier will have to follow higher standard than the drawing of an LED with a series resistor. (This applies to CAE drawn schematics even more so. There's absolutely no reason to not let a student re-draw their schematic in a somewhat sensible, oriented, straight, minimum crossings way, if the way it's currently drawn significantly increases the load of helping them, and stops the would-be answerer from writing an answer. Just as with software, making things tidy often helps finding obvious bugs.)
(To help that a bit, I have a guidance-style self-answered question here, specifically on how to post pictures of hand-drawn schematics: How to add a schematic if my mobile device can't run the schematics editor? )