Several of the people I have the most respect for on this site have replied here. They all make good points, but interestingly don't necessarily agree with each other, which tells me that reasonable people can disagree on this one.
Yes, many commissioners give enough notice, so I am not talking about those situations, and many very good commissioners at times get hurried and perhaps not wanting to disappoint or annoy member owners go ahead with rushed drafts anyway, despite their own RL commitments and things get tangled.
Some, as biglenr points out, announce that tomorrow we are starting the draft and you find yourself about to board a plane, or be away, or having a funeral to do to (I went to four in the past two months, and some of the family visits are in the aftermaths of those tragic losses, including in-laws, so whether it makes me a douche or not, they take priority over even work which has suffered, let alone my own interests), and yet trying to catch up on players.
I suppose I could be researching players right now instead of writing this yes, but then since I thought the request a reasonable one to have considered, and being less of an individualist than some on this site, I thought that my own experience lately might hit some chords with others with whom at the time I may likewise have been impatient, not knowing what they were dealing with. I also am not either a Kantian or a Cartesian: I don't consider time, space or mind to be homogeneous. Which is a fancy way of saying that some days I am better at doing physical work around the house than others, other days I translate books better and sometimes I am sharper than other times at concentrating on the characteristics of obscure baseball players for round 6 of a draft. If I am distracted or feeling like there are too many balls in the air, even if in theory a half hour could be useful, not every half hour is equally useful, since some days a half hour is more than enough for me to get a lot done, other times it is not. I doubt that I am unique in this regard.
I probably will drop a couple of teams, that is probably good advice from crazystengel who usually gives me good advice. But I also know that had these drafts all been next week, and I mean all of them, I could have handled them no problem. I would be tempted to say that having drafts in late August, or for that matter scheduling ANYTHING in late August in Europe (including my two new courses that started this past week) is American-centric (in fact I work for an American college here), since no project, no matter how important, is considered worth starting until September in France, Spain, Italy and elsewhere on this continent. But after all, this is a baseball site, so it should be American-centric. On that point, at least, I will defer.
But my main point, that since I currently have no less than four teams that have been sitting there already in the league, the draft completed, for at least a week each now, while others have not placed their teams in the leagues so we can get started, remains valid I think. This means that others have blocked us starting, which means we would have started at the time exactly, let's say next week to be hypothetical, even had we put the draft off. Instead, we had the draft and this has still not meant getting started.
it could be that a hard line as contrarian23 suggests, is the answer, but taking away a team and finding a new owner, the "death penalty" is harsh if all that has happened is that someone is away, or camping or whatever for a few days or a week or even 10 days. All I have suggested is first polling the owners as we get started to find out their schedules so that such delays will be predictable.