The dpi value has an effect for OFFSET PRESS lithographic printing of photos only. Printed at 300dpi, the photo would have reasonable good quality like on a National Geographic page, but printed at 75dpi it would look pretty pathetic with daily newspaper quality
But If you took a 6000 x 4000 image (dpi value irrelevant) and printed it on a large format inkjet printer to 20" x 30" the resulting print has 200 PIXELS per inch, and the 200 ppi would indeed appear 'sharper' print, while if you printed the same image to 40" x 60" that print has 100 PIXELS per inch,
But BOTH PRINTS printed on the inkjet have been printed at the INHERENT DPI of the the printer (and ignoring the DPI value in the EXIF)...depending upon which Epson model printer, it might have 4800dpi or 9600dpi (dots of INK per inch).