I am far from convinced that defenceman size is relevant at all, but I do think there is good evidence that team shot prevention affects the number of games that goalies play. If you look at all the individual goalie seasons with 70 or more games played since 1983-84 (n=71), 50 of them were by goalies facing fewer shots against per 60 minutes than league average. The average for the entire group of 71 goalies was about 1 SA/60 below league average. Thirty faced a SA/60 rate that was 5% or more below league average, while just 10 faced 5% higher than average.
Looking at save percentages compared to league average gets very similar numbers (51 above average, 20 below average), which suggests that the impact of talent was roughly equivalent to the impact of shot prevention, although shot quality may be a significant factor, particularly in the earlier years in the sample ('80s and '90s).
I also looked at every goalie season with at least 40 games played, and sorted them into four groups based on whether they were above or below league average for save percentage and shots against per 60 minutes. Using the frequencies in each bin from the 70+ GP sample, we can calculate the percentage chance of a starting-calibre goalie playing over 70 games based on those two variables alone:
Save % > LgAvg, SA/60 < LgAvg: 35 / 244, 14.3%
Save % > LgAvg, SA/60 > LgAvg: 16 / 198, 8.1%
Save % < LgAvg, SA/60 < LgAvg: 15 / 165, 9.1%
Save % < LgAvg, SA/60 > LgAvg: 5 / 132, 3.8%
This evidence suggests that team shot prevention is slightly more important than goaltender performance in determining how many games they play. That is, of course, if you accept save percentage as a reasonable proxy for goaltender performance. The shot quality effects in the '80s and '90s were significant for many teams, although typically the correlation suggests that low shots against is correlated with higher save percentages when parity is low. If the goalies on strong defences tended to get a save percentage boost, that would actually strengthen the argument that shot prevention may have a slightly stronger impact on games played than individual goalie performance.
At the very least, these numbers make it pretty obvious that a starting goalie's games played are strongly impacted by his team context. If durability was some separate skill that was unrelated to a goalie's talent or the team in front of them then we would expect to see much less variance based on the two variables being analyzed. This study does not even take into account what is probably the largest factor of all in determining games played, the talent of the backup goalie, or other relevant factors such as whether the team was in a close fight for the playoffs or the difficulty of their travel schedule.
I don't know why the same poster is apparently trying to argue in the same thread both that games played is a good stat for evaluating goalies and that games played are largely determined by the rest of the team, but he's probably closer to the truth on the latter. I personally do not consider games played to be an important factor in my goalie evaluation.