Whether or not it says it, turning that on could make SketchUp slower. Anything that makes the GPU work harder can cause a slowdown. TBH, from the SketchUp files you’ve shared, your modeling workfllow and the sloppiness of the files has more impact on SketchUp’s speed than the Use maximum texture size setting is likely to have.
I know in the past you’ve told us you get models from colleagues. If you are concerned with speed in SketchUp you should invest time in training yourself and your staff to use SketchUp correctly. If your models were built well SketchUp would be faster and you would spend less, or maybe no time fixing problems which would also make it faster. There’s no reason you have to have the kinds of models you’ve shared here. They just don’t have to be constructed the way you have them.