There have been a number of attempts to analyze this statistically over the years, with varying conclusions but generally in line with your conclusions above. See this summary:
http://www.theglobeandmail.com/spor...n-to-pull-the-goalie/article4318101/?page=all.
I think that most studies support the idea that coaches generally err on the side of being too cautious about pulling the goalie.
Apart from the rational, statistical side of things, I think that sometimes a coach pulls the goalie when they are down by 2 or more goals to send a 'message' to his players that he is not giving up and he doesn't expect them to either. I'm always a bit skeptical that this has the desired effect.
And then there are some bizarre situations, none more so than April 5, 1970, last game of the NHL season and Montreal pulled their goalie with 9 1/2 minutes left in the third period, trailing 5-2 to the Black Hawks. The Habs hadn't missed the playoffs in 22 years, a win or tie would put them in the playoffs but a loss would leave them tied for the final spot, with the tie-breaking criterion back then being total goals scored in the regular season (not goals for/against). They needed to score five to win the tie-breaker. So they could leave the goalie in and hope to score 3 more to tie the game, or pull the goalie to score 3 to win the tie-breaker (didn't matter if they lost the game 20-5). They pulled the goalie, but lost the game 10-2.