Connecting to closed paths and having neat corners?

Problem:
I would like to create complex shapes with more than 2 lines intersecting some corners or sides but still retain "proper" edges.
[When attempted with line segments] Is there any way to join these creating correct corners? That would be perfect
And no, setting it to projecting cap doesn't work, and I don't want rounded corners
This is the most universal way I know to accomplish this. Draw the shape outline FIRST...
Then add in interior line paths with butt caps. STILL this doesn't always work (with extreme angled edges for instance)
Still I would like to be able to connect sharp paths to the sides as well (you can't just miter it)
I would love to have been able to just draw up individual lines and click "join corners" but nope, each shape had to be tailored not to have protrusions.
Quite ridiculous, no? Any solutions?

The general problem could easily be solved with a script but i have no idea how to implement it /:
1) cut up all connecting lines and points.
2) join all free pairs of points together starting with the most obtuse ones
3) stroke
4) project complete
I also found 3 ways to solve my original problem:
To join two endpoints in a cluster of endpoints:
direct selection tool > select all points in a corner by dragging over > shift-select (deselects) the lines of the points you don't want > ctrl+J to join.
To join multiple sets of touching lines to form a shape:
endpoints must touch (turn on snap) > select entire shape (outline only) > pathfinder divide > [set desired stroke]
[lines before]
[result]
To join all edges of any shape made of lines:
endpoints must touch (turn on snap) > select entire shape > ctrl+C > pathfinder divide > pathfinder exclude > set to same stroke as before > ctrl+F to paste interior
[box before]
[result]

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