Is It Ever Okay to Leave a Bend Relief Off a Sheet Metal Part?

Yes, but only at a corner where two bend lines meet at 90 degrees and you're
willing to accept a small tear or witness mark at the intersection instead of
a clean cutout. Away from a corner, on a single flange with nothing else going
on, skipping the relief is how you get a torn or wrinkled edge that shouldn't
be there.

Why the corner case is different

A bend relief exists to stop the metal at the edge of a flange from having
to stretch in two directions at once. When one bend line runs into a flat
edge with nothing crossing it, the material at that edge has room to deform
along the length of the bend and nothing stops it from tearing cleanly at the
corner of the flange. That's the geometry a relief cutout solves.

At a closed corner, where two flanges fold up and their bend lines meet, the
metal at the intersection is already going to distort no matter what you do.
CAD flat pattern tools usually give you a choice of corner treatment: "rip,"
"tear," or a relief cutout with a defined radius. Choosing tear at a closed
corner isn't skipping the relief out of laziness. It's accepting that the
last little bit of material at the seam will crack or gap slightly, because
there's no way to form two bends that meet at a point without something
giving. Shops handle that corner condition routinely, and it's not a defect.

Where skipping it actually causes a problem

The failure mode people run into is skipping the relief on an open edge, not
a closed corner. If a flange has a hole or a notch positioned such that the
bend line runs across an unsupported edge with no relief cut, the outer fiber
of the bend has nowhere to go and it tears unevenly instead of forming a
straight line. You'll see this most on flanges that are narrow relative to
the bend radius, or where a feature sits close enough to the bend that the
material between the feature and the free edge can't stretch uniformly.

The other case where it matters is a flange bounded on both sides by
features, say a slot on one side and the part edge on the other. Without
a relief, the bend tries to propagate through material that's already been
partially cut away, and you get a ragged, unpredictable tear line instead of a controlled one. It shows up most on brackets designed
by someone who never watched a part come off the brake.

What to actually check before deciding

Look at whether the bend line terminates at an open edge or runs into another
bend. If it's open and unsupported, add the relief. A simple rectangular or
radiused cutout at the end of the bend line, sized to roughly the material
thickness, solves it in almost every material we run: cold rolled steel,
galvanized, 5052 or 6061 aluminum, 304 or 316 stainless. If it's a closed
corner between two flanges, decide on rip vs. tear vs. relief based on
whether you can tolerate a visible mark at that specific spot, since it's
cosmetic on most brackets and doesn't affect strength.

Stainless work-hardens faster than mild steel, so a tear at a closed corner
on 304 or 316 tends to look a little rougher than the same feature on cold
rolled, worth knowing if the corner is visible in the finished assembly.

The takeaway: reliefs are for edges that need somewhere for the material to
go. Corners that meet at a point don't have that option regardless of what
you cut, so the decision there is cosmetic, not structural.