I picked the displays thing at random off the top of my head but you could supplant one of many different approaches that an autistic child needs.
In the example re the displays, the autistic child isn't going to be screaming and pointing at the displays - but they could be finding it hard to focus, struggling to understand instructions, shutting down and becoming non-verbal. Or alternatively they could be disruptive, loud, refusing work. Neither of these would be obviously related to the displays.
The manifestations of the behaviour are manifold, hence why it's not easy to determine the cause.
Removing displays for a neurotypical child would be counterproductive as children find them useful, instructive and generally uplifting.
If you know a child is autistic, you could immediately look at their environment and identify things that could be changed straight away. It may help a little bit, it might help a lot. But understanding what an autistic child is likely to need, and what they are likely to be struggling with enables the teacher or TA to pinpoint what is driving behaviours. Because those behaviours could be a very, very long way from what the need actually is - and that's why it's so difficult to understand what's going on unless you have a diagnosis.
As I said, you might inadvertently hit on something that helps a child even if you don't have a diagnosis. But you might not understand WHY it's helped the child - and that's important because knowing why something helped means it can be replicated and broadened out. Also, if you don't have a diagnosis it might take you a while to get it right - and you could actually be making things worse if the child isn't autistic.
It's really not the teacher's job to guess. I know it's a different scenario but imagine sending a kid to school with an Epipen and saying to the teacher - no idea what his allergy is, but keep trying and if you spot what it is, give them a jab. Obviously I'm being ridiculous, but the principle is the same - the teacher needs to be equipped with the full information to keep a child safe, whether that's physically or psychologically.