I was going to wait for
@Moon Shooter to put forth what he thinks the analysis would show before replying, but I did some analysis and it seems clear enough the hypothesis is wrong that I'll just post it in advance of him replying.
In my area, our 40+ Adult league just finished the regular season, so now is a good time to take a look at the average player by level and the played average as well.
As I noted in my earlier post, we can look at the average rating for all players rostered, and then look at the played average and see how they are different. So here we go, the first number is the average rating for the flight, the second is the played average.
2.5W - 2.29 vs 2.29
3.0W - 2.72 vs 2.73
3.5W - 3.17 vs 3.19
4.0W - 3.61 vs 3.64
4.5W - 4.04 vs 4.07
2.5M - 2.37 vs 2.37
3.0M - 2.80 vs 2.81
3.5M - 3.24 vs 3.26
4.0M - 3.67 vs 3.69
4.5M - 4.11 vs 4.13
A few interesting observations.
First, the average ratings by flight are not that high, only the 2.5W and 3.0M are above the mid-point of the level. This would seem to contradict your hypothesis that only high rated players play league and the lower rated players for a level give up and don't play. It would seem that the actual case is that more lower rated players play than higher rated players for a level, although this is almost certainly influenced by players playing up.
Second, the played averages are not really very high at all, the largest gap is 0.03 for the 4.0W and 4.5W. The largest gap for the men is 0.02 for the 3.5M, 4.0M, and 4.5M. This would seem to indicate that there is a very very small bias to the higher rated players getting in the line-up more often than lower rated players. Certainly the lower rated players are not "rarely" played.
If one wants to posit that including players playing up skews things, I did the same analysis with only at level players included:
2.5W - 2.29 vs 2.29
3.0W - 2.77 vs 2.74
3.5W - 3.25 vs 3.20
4.0W - 3.69 vs 3.66
4.5W - 4.13 vs 4.08
2.5M - 2.37 vs 2.37
3.0M - 2.84 vs 2.82
3.5M - 3.30 vs 3.27
4.0M - 3.75 vs 3.71
4.5M - 4.21 vs 4.16
Here we see that both numbers go up in every non-2.5 case as you would expect, however, the average rating across the rosters goes up more than the played average! And now the played average is
lower than the rostered player averages!
The conclusion you can make from this is that it is not the higher rated players that play more, but instead the lower rated players that do, completely at odds with the hypothesis that lower rated players are rarely in the line-up.
Now, it may be that the top teams in a flight do play their top players more, so I took a look at only those teams advancing to local playoffs. For these it was:
2.5W - 2.31 vs 2.31
3.0W - 2.81 vs 2.81
3.5W - 3.31 vs 3.32
4.0W - 3.73 vs 3.71
3.0M - 2.89 vs 2.90
3.5M - 3.33 vs 3.34
4.0M - 3.81 vs 3.84
4.5M - 4.24 vs 4.24
A few things to note here.
First, the ratings go up for the teams that are advancing to playoffs as you'd expect, roughly 0.04 to 0.06 higher, which goes to the point I made earlier that some teams are simply stronger at the start of the year and more likely to advance, and we see that they do, yet this doesn't prevent the other teams from participating and playing.
Second, even for these contending teams, there isn't much of a gap between the played average and the average player on these teams. Just the 4.0M are 0.03 higher for their played average and the others are the same or within 0.01, and the 4.0W even have a lower played average.
This is in one area, and thus the results may not reflect what happens in other areas, but it is interesting that even my thinking a 60/40 split was what we might see wasn't accurate. Perhaps player behavior in other areas is significantly different, but this analysis clearly shows there is no flight away from league play for players lower rated for their level and no bias in not playing them once on a team.