Can we post a replay of say, a Starcraft 2 match, and have the question be about what I should have done differently?
That's very personal question not very valuable to other people.
If you had a question about dealing with a certain strategy and wanted to link a replay to help illustrate the strategy you were having trouble with, that might be appropriate, but you'd still have to explain what it was, and what you tried to do so the question was accessible to people who couldn't view the replay.
If the question can't stand alone with out the replay you shouldn't be linking it.
I think the larger issue, when combined with the singularity of such an inquiry, is that there's very little of an attractive "question".
This is similar to people on SO who just post a huge wall of code and want to know "what is wrong with it". People aren't going to want to sift through your stuff without even a torch to guide them to your problems. It's actually worse in the case of a replay, because now the answerer has to consume at least as much time as the replay lasts.
You need to make questions worth the time of people to actually look at them. A replay question is isolated to your situation which means not many people will be inspired to look at it. Fewer people looking at a question means fewer people to look at the answers, so the answerers are getting very poor mileage for the effort spent in analyzing your stuff for you. That's not a very attractive prospect.