You guys are LEO and in a different world. I have been a part of a church security team for ~10 years. In comparison to most we are pretty well organized and do train. I am also a USPSA shooter who is A class in 3 divisions. I help with training.
In this small subset I definitely see new members who come to the team shooting better on our standard drills. I also see the long term members who switch have improvements. These are not night and day, but 5-10% is 5-10%.
I agree there is no replacement for training, but most people aren't going to train near enough. If the dot helps it helps. I believe Karl Rehn did a study a few years ago on dots vs. irons and found the lower skill shooters benefited to a greater degree than more skilled shooters. I agree completely (from my admittedly tiny and anecdotal sample) We recently had back to back training weekends. I compete with and carry irons primarily. I shot near identical scores with irons vs. a dot but I don't there is anyone else who could do that on back to back days. The irons are just require a lot more attention and training.