What I did was take the 50 catchers over 2014-2016 who had received the most pitches down in the lower third of the strikezone and outside of the strikezone to the sides and below of that strike area. Those strikes turned balls and balls turned strikes were converted to a runs per 1000 pitches metric. The fewest number of pitches caught in that area was Kevin Plawecki with 4056. The greatest was Salvador Perez at 24582. The top two catchers by far were Tony Wolters (39.9 runs saved per 1000 pitches based on 4222 pitches) and Francisco Cervelli (39.0 rs/1000 based on 15169 pitches). Dioner Navarro (-44.7 rs/1000; 10894 pitches), Jarrod Saltalamacchia (-42.3 rs/1000; 6285 pitches), and AJ Ellis (-40.5 rs/1000; 5002 pitches) were by far the worst.
Just looking at those numbers, Wolters is the second shortest catcher in the group and Cervelli is right smack dab in the middle. However, Navarro is the shortest guy on the list while Salatlamacchia and Ellis are 6'3" and in the top 13 for height. That all does not exactly mean all that much. What might make this work a little better is to batch this into four groups: 5'10" and shorter, 5'11" and 6', 6'1" and 6'2", and 6'3" and above.
% abv avg
5'10" and <
5'11 and 6'
0 +/- 15
6'1" and 6'2"
4 +/- 20
6'3 and >
-10 +/- 21
Visually, there appears to be a trend line, but it is not significant. ANOVA also is unimpressed even though the average makes the 6'3" and above batch look different. Additionally, the percent above average looks pretty unremarkable for players above 5'11". If one could fathom a reason to do so, eliminating Saltalamacchia and Ellis from the tallest group would result in a -3.2 +/- 16. In other words, it might be what really powers these appearances of a trend are the existence of a few remarkable players pushing that trend. I tried to compare them by their performance against their height to no avail. The worst quartile were on average taller (6'1.5"), but only differed by an inch with the best performers (6'0.5").
It may well be what people are observing is that catchers who are poor at framing pitches low do other things quite well. Part of this might appear to be a size issue because those other things are related to size, but that is more a tangential correlation than an actual correlation. In other words, by taking into account for height you are measuring something that is related to why some players are poor lower pitch framers, but have not actually figuring out the true reason for it.