Make Intertwine into a tool, available from a tool panel.
Objects on Path is a tool, and it creates a dedicated object... and does nothing else! all the operations with this new object are performed using the Selection tool...
Meanwhile, an Intertwine object would need a command, Object > Intertwine > Edit (or a button in the Control panel) to be edited — which just enabled the hidden tool! Make it a real one!

This has been helpful in several situations for me.

George, I agree with you on these.
However, since the tool is now released, we better stick to separate requests, to get proper statistics on what to improve with Intertwine.

Please take a look at these new requests and vote for those you find worth it:
https://illustrator.uservoice.com/search?filter=ideas&query=intertwine
One of them is exactly about the thing you write about.
Feel free to add your own!

Further to my previous comment about needing to be able to re-select and edit the original selection. Why not make the selection an object itself, like a mask? That way you can precisely draw where you want the intertwine to occur, rather than a shaky lasso selection or a rigid box. You would then apply the intertwine and change the layering of the other objects. Would be very easy then to go back and edit it (and the layering of the other objects) as required.

What you call "Artifacts" I call a cool option, to have the intertwine disappear halfway through another object, making them look like they've intersected! Can draw the selection to sort of paint the objects on top of each other.
What IS disappointing, is that I can't seem to reselect the bounding box for the original selection I drew. When intertwining more than two items, it works well at the time of the initial selection, to move objects forwards/backwards in the layering while the bounding box is still selected/visible. But if I go back later to EDIT the intertwine, I have to redraw the selection box, which won't match the original at all. THIS results in weird artifacts where the two different selections are now slicing the object into multiple parts. You need to be able to select the initial selection box, to then change the order of the objects within.
AND, it appears that you have to do this for every change - the new box that you just drew disappears once you right-click/move just one of the overlapping lines. So you really need to be able to reselect the existing bounding box.
(Would also be VERY cool, if you can modify the selection itself. Say you change the width of an object's line, and it now extends past the original selection area, resulting in the partial overlap artifact. Just modify the selection to enclose the updated width, and it's done.)

Next day, tried again fresh.
The What's new text described using the shift key, but it is still the lasso tool to select the area in which to accomplish this. Haven't tried today with the multiples as in the demo video, but yesterday couldn't make the object above, below, etc, rearrangement. With blue behind red behind black objects, first intertwined the red with the black, Second the blue with the red, and last the chord segment (pointed to with orange arrow) of the red also brought above the black shape

Yes, I confirm Richard’s test, a Repeat out of a simple Intertwine object first leads to 'Can’t preview' issues and then to a crash. The crash report is sent.

This worked well interleaving rings with the earlier v26.4 beta

Need to update this page with discussion as per Changes since last opened in v26.6.0.526
tried to make a pattern from an initial partial-rearranged object that had two overlapped paths and the beta would crash frequently however I tried to acco

Dang, I like this. This solves a pretty frequent help request that we currently have to teach beginners a *bunch* of stuff to do.

Maybe this should be part of a Depth Arrangement Tool instead of another thing crammed in the Object menu?

(Which begs the question of what else would such a tool do: access to basic send to front/back, as well as put all selected objects in front of the topmost/behind the rearmost selected objects (I do this a LOT via some scripts), and reverse the stacking order of selected objects is my suggestion for things that would all belong in a Depth Arragnement Tool.)

Keyboard shortcuts for the options in the right-click context menu would be most welcome!

Its better to use following algorithm:
select several object,
group it,
select desired anchors of objects inside group,
use 'Object / Arrange ' menu.

Looking forward to testing this feature out to see if I could incorporate it into my workflows.

What happens if I change or even move the art?
If I modify the ribbon shape and it stops fitting in the designated area?