Imagine a tool that sits in the Tool Panel used for complex alignment. When you click the tool, Illustrator would enter an Align Mode that changed the way some things operate the way Isolation Mode changes things when activated.

In Align Mode, a panel would be displayed with options (below) Your cursor would allow you to select not only the elements you want to align, but also the point of reference for alignment. You would see the standard boundary box appear when selecting an element, but you could click one of the 9 reference points on the bounding box to indicate that you want to align that element by that point. Once you have all of your elements selected, you can ALT-click an element to act as the Destination. It will display the bounds box for the Destination element and let you pick the reference point from the 9 reference points in the bounding box.

In a side panel, you would have options that controlled how this would happen. For example. you could have the Ghost Result option selected to show what your alignment would look like by aligning the selected elements to the destination as ghosted previews (transparent). But you could also Ghost Source so you would see solid previews of your aligned items while the original positions would be ghosted. When it looks the way you want, click the apply button to apply the alignment.

This is one small piece of a much bigger and much more robust tool that would allow you to do all sorts of advanced alignment. Like Transform Alignments that matched size and/or rotations. It would allow you to do non-lineart distributions for distributing things like position, size, rotation. It would also allow you to see a distribution path between elements that you could micro adjust before applying. You could even change the distribution model so it did non-linear easing. All of this in one tool with the Align Mode. When you activate a different tool, you would exit Align Mode just like exiting Isolation Mode.

I have looked at all of the align/distribute user voice requests and every single one would benefit from this system. Please contact me for more information. I'm working on a demo to show how easy this would be.

Yep, waiting for a demo then. It’s somewhat clear, but, as always, a bunch of even simple images would help.
Some of these things you describe are doable with specific plugins and scripts... but none can permanently assign specific alignment pivots.

Plus this reminds me of this more narrow request about Alignment groups: https://illustrator.uservoice.com/forums/333657/suggestions/35643463 — for some things within a group to be ignored when aligning.

Simple.

You create a series of symbols that have different sizes. You know you want the instances of the symbols aligned in this manner:
All instances of symbol A belong on the left side of the artboard, but aligned to the right and distributed vertically.
All instance of symbol B belon on the right side of the artboard, but aligned to the left and also distributed vertically.

So you have a bunch of instances of Symbol a in various sizes and treatments and the same for Symbol B. Setting up this alignment strategy once makes it foolproof in the future. Resize the content of a Symbol A and your entire layout is ruined. Start from scratch grabbing all the Symbol As and align/distribute. Or press Play on that alignment strategy and watch all symbols As get selected and aligned then all Symbol B's do the same. Voila. Tons of work saved.

Also, think of alignment strategies like graphic styles. You setup your forms so that your labels are aligned right and the square for the input is aligned left.

You do hundreds of these fields when you hear that what they would prefer is to have your field labels aligned left, on top of the square for the input.

Normally, you would have to go through hundreds of changes. With an alignment strategy, you change the details of the alignment so that [labels] alignby Bottom Left to [fields] by top left with a 5px gap. Press apply and your entire form is modified instantly. Save that as a new strategy and flip back using the old strategy in a mouse click.

Part of the proposal I am working on also allows for property sorting in alignment strategies. So imagine you have an infographic with lots of different sized elements. Those elements are sized according to their popularity. An alignment strategy could align all of the elements distributing the space between them vertically, but sorting them by size automatically. All the tiny ones up top, big ones below.

You get a bunch of new images you have to add and rather than manually inserting the images and fudging the alignment, you simply select all of the images and apply the alignment strategy--boom they are sorted, distributed and aligned. Hours of work saved.

There are lots of other details to this idea that I am hoping someone at Illustrator will listen to one day. I've been working on it for a long time and It's pretty close to being presentable. Just need to get some figma stuff fixed for demo.
Thanks for listening.

I wonder what workflow or task requires a method like this? Why realigning some object later again? Just curious.