Usually, routers stay on a fixed channel and the wifi cards scan the available channels and pick the one with the strongest signal. You rarely, if ever, want your access point to be changing channels. For example, in my home network, I need to have the router fixed at channel 11. If I don't, I get TONS of interference from the 2.4 GHz phones.
You've got an interesting observation, and to be honest I've never played with changing the channel when connected. However, it is very easy to scan all channels for an access point, so I guess I'm not sure that knowing what channel an access point is using is helping any.
For me, the bottom line is that SSID broadcasting seems to help with getting the connection and since not broadcasting the SSID doesn't even provide negligible improvements in security, it simply doesn't hurt to do it.