For singular dots in space your argument would be valid, but real objects are often more complicated. If the eyes can’t reliably lock onto the same spot along the X-axis due to a repeating pattern or a complete lack of detail along said axis, tilting the head shifts the whole situation and allows the eyes to zero in on a fixed point to perceive depth. An extreme example: If you look at two horizontal featureless lines (offering no details along their length to lock onto, brushed metal railings for example) positioned one behind the other, running perpendicular to the field of view in the direction of the X-axis. The only way for depth perception to work here is to tilt the head to introduce a difference along the Y-axis. Repeating patterns with the right spacing (e.g. grids, lattices) in that same plane can also confuse depth perception, in which case the head tilt often helps.
Another (marginal) benefit of head tilting is the fact that as the head rotates, the eyes physically move, possibly revealing additional detail that may have been obstructed from the previous vantage points. All this for a much lower energy expenditure than the whole animal moving itself.
Oh and one thing that popped into mind from personal experience as I am writing this: In darkness tilting the head helps discern between shapes that are just lingering on your retinas after looking at a brighter thing earlier (rotates along with the eyes) vs. dim things that might actually be there right now (stays in the same orientation relative to the surroundings).
It’s not that the triangle doesn’t exist, but that the brain has multiple options for forming said triangle, only one of which results in the real image. Threw the following together to illustrate:
I was looking at a grid lattice wall paneling just this week which had the same effect. If the pattern is perfectly uniform, the eyes can’t distinguish between different features in it. The whole situation is a bit comparable to a stereoscope. Shifting the eyes out of plane with the pattern causes the false images to split vertically while the one true image remains. This isn’t an issue most of the time, but it does demonstrate how some situations invalid for stareopsis can be tackled with a simple head tilt.
Rangefinders aren’t usually looking at patterns in walls for example. Aircraft or ships don’t create uniform enough patterns. Yes it’s still an edge case, but I just wanted to explain my point that tilting the head does offer the brain more to work with, which in some confusing situations can be critical to correctly perceiving the situation.