Here's a little ramble. Feel free to ignore it (most have done in the past).
I taught sax for 30 years. Retired 6 years ago. Mostly private tuition but some school stuff. Most of my students were children.
In 30 years virtually all of the kids and most of the adults were completely uninterested in jazz, or any other variety of improvisation. Despite this, i tried with everybody to get them to do at least a little bit of noodling without the dots in front of them. I'd guess at least half of them (probably more) utterly refused. Most of the ones that did try gave up pretty soon. Apparently because they thought they were rubbish at it.
Now, bearing in mind that many of them were complete beginners at sax, why were they perfectly happy to be rubbish at reading but not at not reading? It's as if they expected to be like John Coltrane (who they wouldn't have heard of) from the start. And if they weren't, well then, they were not going to bother.
I should point out that no theory was involved, so they weren't bogged down with chords and scales. All they had to do was to be able to play a few notes. Just one or two to start with, but still most of them wouldn't attempt it.
I've never really understood why. It's practically the exact opposite to how I started. I was improvising as soon as the sax was in my hands.
Anyway, noodling is good. Do it. Listen to what you're doing. Forget about theory, chords, scales and all that stuff - it just clogs your brain. Just play. You'll get better at it.
Here's a little bit of improvisation that isn't jazz.
app.box.com