This would be so helpful when selecting multiple objects along custom angle lines.

An here is the GIF

I have a very narrow method to select objects intersected with a path.

It has a lot of restrictions though: objects to be selected should have flat fills, do not intersect each other, have no strokes, should not be live texts, blends, brushes, etc. Basically, it suits the artwork provided by Rob Hutchings below.

The result is two groups. Some very minor garbage paths get generated sometimes. VFA plugin by Astute Graphics deals with most of them.

Take a look at the GIF attached.
Steps are
1. Lock everything but the art you want to process ant the outlined stroke (the background in the GIF already is locked).
2. Enable both options in Pathfinder panel.
3. Draw paths which intersect objects you want to select (the GIF already has them drawn), and set some stroke weight for them — they have to have some weight, and it is going be used to define intersection.
4. Outline the stroke.
5. Select all.
6. Pathfinder > Add. This will weld the former stroke with the objects.
7. Select the welded piece only — the best way is to pick Group Selection tool and click the piece in the fill, or Isolate the result with a double-click with a Selection tool (requires this option to be toggled in Preferences).
8. To minimize artifacts, apply Offset Path to the piece — just slightly, don’t cover the gaps!
9. Copy the result.
10. Undo Add and delete stroked paths — we won’t need them again.
11. Paste the welded piece in front. Now we are going to use use it as a separator.
12. Select All and clip the object with a welded piece.
13. Hit Merge twice (the second hit often fixes some small errors) — now you have only the objects you wanted to select, as a group.
14. Copy it and Undo to the step 11, when you have the original art and the welded piece in front of it.
15. Select All again and now just hit Merge twice, without clipping.
16. Isolate the result and delete the welded piece — now you have original objects behind the monolith merged with it — delete them.
17. Despite we set options in Pathfinder, we still have objects with no fill and no stroke inside! Select one, use Select Same Fill command and delete them too.
18. Exit the isolation and paste the art we had in the buffer since step 14.
19. Now you have two groups — one with object you wanted to select and those you didn’t want to select.

It’s hardly can be automated with actions or scripts — it requires some aiming, but it can be much faster in some cases, than manual selecting objects one by one.

I'd settle for this but would prefer to be able to convert any path into a selection. Photoshop has been able to do this since forever and it seems completely bonkers that the vector program cannot!

I currently need to make a precise diagonal selection to duplicate these shapes to fill the newly widened promenade. The lack of a Photoshop-esque Polygonal lasso tool or convert path to selection function makes this task really cumbersome!

Why didn't I group one column before I transformed it in the first place ... I know ::facepalm::

A more precise way to select objects other than lasso tool. A polygon selection tool like Photoshop would be perfect.

I regularly prepare projects in Illustrator, in which I have to mark large, complex groups of objects with a lasso tool. It would be a lot easier for me to work if I could select objects using polygonal lasso in Illustrator. It would save me many hours of work!

Vector lasso tool, which can also make straight lasso lines between lasso points, similar to what pen tool does between anchor points.
Problem: Selecting multiple objects or anchor points within a complex shape consisting of straight lines, or adjacent to an inclined straight line, is a difficult using the present lasso tool. Please consider the simple example of selecting objects within a triangle - both the rectangular direct selection tool and the lasso tool are useless for that.
Suggested solution: The present lasso tool could be changed to operate in point-to-point mode while a certain key, e.g. Alt, is pressed, and in free-hand mode (present lasso tool) if no key is held. Or vice versa.

A polygonal lasso tool to make it easier to find and group sub-paths in a group or on a layer. A mere corner of a path is needed to add the path to a group, selecting adjacent paths that share a corner point in order to group them would be a lot easier with a polygonal lasso tool.

Absolute madness that this still isn't implemented now.

YES! To not have polygonal lasso is a cut back!

Yes! It's absolutely fascinating to me how this is not a standard feature/tool in Illustrator!