First -- I am not a SWAT operator. I do work with them frequently, and the unit I am a part of does low to medium risk entries. I've been in various positions on entry teams in more than 100 search warrants. In other words -- I do have some idea of what it's like to go into a house, over the strenuous objections of its residents.
Second -- I am not automatically assuming that everything was done right or perfectly. I don't know why they banged a house with young kids in it, for example. Most SWAT units won't do that, without a very good reason.
Third -- I've been way too close to being in a position much like that. We recently did an entry where we ended up compromised, meaning that they saw us approaching, and made a more dynamic entry than we usually do. As we cleared the house, one of my partners and I entered a room. As we cleared our areas, he came across a closet, and I suddenly heard him giving orders to someone. I turned to support him, and the person in the closet finally came out... It was a young girl, and yes, we were both pointing guns at her. Not a good feeling.
OK... All that out of the way, this is absolutely a tragedy, and the cops involved are, I'm sure, tearing themselves up about what they could have done differently. I don't want to speculate on what could have happened; there are several possibilities, and it seems a good chance that there will be a pretty solid explanation after the investigation.
It was asked why are SWAT entries done in that fashion, especially in a case where you know where the guy is. The whole goal of any SWAT operation to use the least force to take control of the situation necessary, keeping everyone -- especially the cops and innocent public! -- safe. But the rule of any entry is Speed, Surprise, and Violence of execution. In short... shock and awe. If everyone inside is caught literally or figuratively with their pants down, there is much less chance of encountering resistance that could get someone hurt or killed. On top of that, they rely on intelligence gathered about the target. In a perfect operation, they know exactly how many people are in the house and where they are, the layout of the house, and more. They go in with a carefully devised plan (ready to improvise when it falls apart!), and everything is over quickly.
Why not wait the guy out? Depends on the circumstances of the case, and where it is. The ATF was, in my opinion, rightly criticized for their choice of tactics at Waco; everything there seems to have lent itself to snagging Koresh up as he left. I don't know the details of the case in Detroit, or the community where it happened. There are places where we won't even think about waiting for someone to exit, because there is nowhere safe in the community to set up for them; I'm quite confident that Detroit has quite a few places like that! Also, nobody wants a hostage situation, and that may have been a concern of the police in this case.
It's certain that there will be an investigation, and I hope it's fair and impartial -- not a witch hunt to blame the cops, nor some attempt to cover up any mistakes or failures on the part of the cops.