While it is easy to generate Revit door schedules it is not that simple to correlate them with legends. This is a frustration to the industry in general but there is potentially one optional workaround that would reduce the length of time spent on managing the legends.
Consider the legend below. While it is easy to place the door legend component in planned and elevation there is no way to tag or label the door with any information, so any identifier must be added manually.

If you have a standard set of doors you reuse from project to project the process might be simplified, but each project usually brings its own challenges, and quite often the doors are not the same as in a previous project. I recommend you create the door legends toward the end of the project after you have purged any unused doors.
My current leaning is to load an image generated from a door schedule directly into the type image of the door type.

If this is done for every typical door type, then generating the legend is almost superfluous. Care must be taken when any new door types are created because the images, especially if they are dimensioned, will have to be corrected.
If you want the generation of the legend component to be automatically available as an image to the door schedule, please vote for the idea here. It would then operate much the same as the rebar schedules in Revit 2024, in which the shape image can be automatically displayed.

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