Unable to Adjust Inset Spacing in Text Boxes: Settings Blocked

Good point, so the original question I believe was centred around the insets not being available to what looked like a normal shape, only got the information for the Inset and Left, Right, Top, Bottom not available, in this case, convert to shape works reset it, and then you can insert those insets.

What are the options if you actually want an irregular shape?

Yes, that's one approach, a separate shape behind it. 

Alternatively, if it's text, you could use left and right margins - and use Baseline Shift to move the text away from the top. - but irregular shapes you can only have an overall inset.

That's your regular inset on a regular frame

With irregular frames you only have an option for an inset

Then you need to change your paragraph settings

Here I have a 2mm left indent

4mm right indent

and baseline shift of -2mm (-5.669pt)

Or you can create a text frame over your Irregular Shape

For example - this is text inside the shape

But changing the text could cause it to overflow and maybe you want the shapes all the same size

So a separate textframe over it could help resolve the issue

Here - adding €399.99 into the text frame oversets it because it's too much text, I don't want to widen it to keep the shape the same size.

So the bottom one shows a separate text frame over the shape where the text frame constraints make it hard to use.