Shooting in 3D costs are said to be 2-4 times that of 2D costs. Mind you, that is the costs of shooting the film, not the whole budget. It's mainly because you have twice the amount of data: for every frame you'll have to do everything twice, once for each eye. Furthermore, the whole filming workflow must be updated. You have bigger, more expensive cameras, including setting up the cameras correctly for each scene to avoid headaches for the viewer.
Back in 2010 (I couldn't find newer sources) it cost between $50k and $100k per minute to convert 2D to 3D. Converting Titanic was the most expensive conversion I could find and cost $18M. I imagine it can only be done a lot cheaper after 4 years of experience. Clash of the Titans, which was said to have horrible 3D, costed only $4.5M back in 2010 already This film had a budget of $125M. So the conversion costs are just a fraction of the budget, but it adds substantial costs to the ticket in theatres.
So it is not cheaper to film in 3D compared to doing a "simple" conversion.
Some key points from wikipedia on 2D to 3D conversion:
- Stereo post-production workflow is much more complex and not as well-established as 2D workflow, requiring more work and rendering.
- Professional stereoscopic rigs are much more expensive and bulky than customary monocular cameras.
- Some shots, particularly action scenes, can be only shot with relatively small 2D cameras.
- Stereo cameras can introduce various mismatches in stereo image (such as vertical parallax, tilt, color shift, reflections and glares
in different positions) that should be fixed in post-production anyway
because they ruin the 3D effect. This correction sometimes may have
complexity comparable to stereo conversion.
Stereo cameras can betray practical effects used during filming. For example, some scenes in the Lord of the Rings film trilogy were
filmed using forced perspective to allow two actors to appear to be
different physical sizes. The same scene filmed in stereo would
reveal that the actors were not the same distance from the camera.
By their very nature, stereo cameras have restrictions on how far the camera can be from the filmed subject and still provide acceptable
stereo separation. For example, the simplest way to film a scene set
on the side of a building might be to use a camera rig from across the
street on a neighboring building, using a zoom lens. However, while
the zoom lens would provide acceptable image quality, the stereo
separation would be virtually nil over such a distance.
- With the lack of stereo content, 2D to 3D conversion is the only way to meet demands of the 3DTV industry.
- Stereo conversion is needed for converting older popular films – such as the Star Wars series, Titanic, and so on.
- Even in the case of stereo shooting, conversion can frequently be necessary. Besides the mentioned hard-to-shoot scenes, there are
situations when mismatches in stereo views are too big to adjust, and
it is simpler to perform 2D to stereo conversion, treating one of the
views as the original 2D source.