Try selecting multiple paragraphs on a website, for example. The behavior is generally unpredictable and requires lots of fiddling. Deselecting text requires yet more work. Double-tapping a word should select the word itself, but that's often not the case. And it's not just websites where the DOM adds complexity; the same erroneous behavior exists for native apps.
For example, open an iMessage text and paste one or more images. Now go back and try to edit existing text. Or add new text. Moving the cursor and text selection is non-deterministic and requires scrolling and fiddling, manually adding line breaks, and then removing them just to get the formatting correct.
In other words, as the OP mentioned, text editing has been problematic on iOS/iPadOS for ages. Interestingly, VisionOS, which perhaps has the most challenging input and editing environment, has managed to resolve many of these issues.
While initial VisionOS releases were buggy and nearly unusable, it's rather striking that you can now use your eyes to move and edit text with more precision than what's possible on iOS/iPadOS--which tells you how much room there is for improvement.
I never until today thought of pasting images. I always add them using the Photos button, then just write my message as normal.
I see now how moving cursor around rich text with embedded objects is glitchy, and I imagine if you deal with that on daily basis it could be frustrating.
However, none of the other issues you or others described seem to be reproducible on my phone. Double-tap to select, or tap to place cursor, seem to just work in regular plain text areas.
A couple of times per week it happens for me that the cursor chooses to land on the wrong side of white space or such, but that is infrequent enough and easy to fix that it does not bother me.