What is the largest print out that has diminishing return in image quality?
A rather abstruse question, IMHO.
Surely, as has already been said or implied, it depends only upon human visual acuity. Since the OP makes no reference to viewing conditions, we can safely take an average value for visual acuity of 0.29mrad (1 minute of arc) for a distinguishable point. And that would be the answer, if the question in the OP were worded differently.
(By expressing visual acuity as an angle, we remove all that obfuscation due to differences cameras, lenses, printers. Also, by expressing the angle in radians we can use the small angle approximation when considering actual dimensions or distances.)
Thus we find that "largest print out" should be interpreted arguably as "the largest ppi", in order to answer the question and ppi, unfortunately being a dimension, involves the viewing distance. I won't insult you with an example
So instead, taking 0.29mrad for a distinguishable point, the points per radian becomes about 3450 (or 60 points per degree of visual angle), and
that is the value below which there is a diminishing return in image quality.
mrad = (1000)/(dist(ft) * 12 x frequency(ppi)) approximately. From which we can say ppi = (1000)/(dist(ft) * 12 x 0.29)?