Export As in Photoshop doesn't seem to work with large document files. Am I right?

Good point. Create an action, and the whole process only requires one keystroke.

FWIW, I have a couple of actions for this. Resize > sharpen > Save For Web > close original without saving.

Export still doesn't record in actions (!), so it has to be Save For Web.

You don't have to save the duplicate (unless you want to keep it), just close it without saving.

Make a duplicate of the original (Image > Duplicate), then use Image > Image size to resize it to the pixel dimensions you want to use for Export (or at least significantly smaller than the original). Then use the duplicate for exporting.

Alternatively, resize the original temporarily, but you must then remember to undo the resizing after exporting.

If the image is for printing, use Save As instead. Export is for creating images for screen viewing, and will strip out the ppi value, as well as most other metadata. 

Export is intended for web and mobile devices - small files. There's a size limitation around 8000 pixels or so.

For large files, use Save As. That's the standard output method in Photoshop.