(LUT = color correction with a preset

)
That's not always the case. In fact, if you're applying a LUT and calling it your color correction and exporting, you've shot yourself in the foot.
LUT to go from LOG C to Rec 709 isn't color correction, it's simply a color conversion between color space.
Correction goes FAR beyond that.
Also... color correction WITH a preset. Please no one ever use a C to 709 LUT that includes a grade. LUTs that are used to give a stylized grade have already started your grade, and baked it with your color space conversion.
1) You just lost control of your color space conversion.
2) You're using a indie-bait LUT. (These are LUTs created for the purpose of appealing to indies promising the "cinematic look". These are NOT one stop-shops for post-production coloring.)
Stylized LUT? Yes, they exist. Every colorist will most likely have a collection of them. I myself have about 15 of them I've created that fit into genres and moods that a lot of indie filmmakers seem to like. They have only a few very broad uses and are in no way the last part of a grade, nor do they do ANY correction.
1) Export them combined with a 709 color space baked for on-set PREVIEW of rough final picture.
2) During initial color session to show possible options.
3) Rough starting points for simple grades.
I would never use one of my stylized LUTs on a project that was paying me. Any serious project (broadcast, festival, or feature) I would have corrected and graded from scratch. The color space LUT would be the ONLY one used.