I agree with Dellow's general sentiment that goaltending evaluation is generally all about the large sample size and evaluating goalies based on single games is a poor strategy, but at the same time I think there are some legitimate merits to "riding the hot hand" as long as it is done responsibly and within reason. I think there is a clear and understandable difference in mindset between the evaluation processes of a GM and a coach. A GM wants to measure talent, a coach wants to measure talent and motivate his players to succeed through the options at his disposal. I'm not sure a coach can be the ultra rational type because they do have to take into account the fact that they are leading a group of personalities on the team and want to make sure that the incentives are always properly aligned.
A hockey team is a group of competitive individuals that all want to play, and it is pretty much always in a team's best interests to encourage some level of internal competition to keep everybody sharp. It is tough to have a legitimate internal competition when you are going to just keep giving the same guy playing time whether they have earned it or not. When there is a situation where there is an elite goalie playing with a replacement level backup then it doesn't really matter what the coach does, even if the top guy is struggling you give him the minutes to play into shape and nobody is going to argue. But if there is no clear #1, or an inexperienced guy who was supposed to be the starter is struggling (as Devan Dubnyk is in Edmonton, the occasion that prompted Dellow's post), then it's difficult to handle it politically if you want to keep riding a guy who is returning mediocre results, both externally to the media/fans and most likely internally in the room. It can be an easy narrative to say that a team trusts or does not trust their goalie, and I'm not convinced that the effect is all that large, but there is at least something there, and coaches tend to be the perfectionist types that want to account for every single factor (the kind of thinking that leads to putting two RHS centres on the ice for right-side defensive zone draws late in the game, for example).
There's a saying in football that the most popular guy in the city is the backup quarterback. Hockey fans can often latch onto the same kind of thinking in that the unknown abilities of the up-and-coming prospect or the journeyman AHLer might be preferable to the overly scrutinized flaws of the incumbent #1. The difference between the sports is that a backup QB often never gets to take the field, while a backup goalie will always play at least some games. In the grand scheme of things, if a team chooses to slightly overplay a backup or give a journeyman goalie a few not-necessarily-deserved starts because he is the "hot hand" and the main guy is struggling, that has very little impact on the team's overall chances across 82 games. Even in a scenario where the starter is elite (say, .920) and the backup is replacement level (.say, .905), a quick estimate indicates that an extra 5 games for the backup instead of the starter will cost the team about .001 in overall expected save percentage, which is a little less than one full point in the standings for a team with a typical rate of shots against.
That appears suboptimal, but if it has even the slightest effect in terms of motivating the top guy to improve his focus or work on his game then it might even be a positive move, despite the fact that the depth chart rankings make it overwhelming likely that the replacement goalie is in fact less talented. Who wouldn't take a tradeoff of -.010 for 3 games in exchange for +.001 over 60, for example? There's no guarantee that you get those results, of course, and I think the reactive nature of goaltending means that effort and desire is less correlated with success than at other positions, but I'm not willing to completely write off the benefits of competition either.
There can be cases where a coach gets legitimately carried away by the "hot hand" approach. Probably the most dangerous one with the highest potential for serious consequences is when a goalie starts his career in the league or with a new team hot, and then coasts on that reputation for a long time before his team figures out that he isn't all that good. In that case a reactionary coach would actually be preferable since they would be more likely to play other options rather than end up with an entrenched starter possessing overrated talent. I also particularly hate the setup where a goalie who wins gets to stay in net for the next game regardless of how well he played the previous night, simply because it is based on such a high degree of luck, but that usually only comes into play in tandem situations where there probably isn't that much between the netminders to begin with and there wouldn't be much cost to even the most random of strategies. On the whole it seems to me that it should be largely self-correcting. If there is a large talent discrepancy, then it's probably going to reveal itself pretty quickly anyway, and if it doesn't reveal itself because the inferior guy is running hot then that's not really a problem, is it?