An important item here seems to be the 'can' in 'everything that can happen'; as opposed to things that /can't/ happen. If a meteor has been orbiting for millions of years in a course that leads it so that, tomorrow night, it lands on my house, there is very little that the various differences across the timelines can do so that it's not going to land on my house. Any timelines in which I'm anywhere near my house at that time - and that's going to be most of them - are ones where I'm going to end up dead. However you want to divvy up the timelines involved, there will be a greater proportion of them where I'm dead than I'm alive.
This is the same reasoning which leads to the conclusion that quantum suicide/immortality is a bad idea to try out; and that it's generally a good idea to maximize the swathe of timelines in which future-you remains alive and healthy. There may be a net sum to all those infinitesimal timelines when added up - but that sum isn't necessarily going to be '0'.
Since you can do only things which can happen, you actions are unable to change the set of things which will happen to multi-you across all timelines.
I haven't been able to find the source of the idea, but I've recently been reminded of:
This is, of course, based on the Multiple Worlds Interpretation: if the lottery has one-in-a-million odds, then for every million timelines in which you buy a lottery ticket, in one timeline you'll win it. There's a certain amount of friction - it's not a perfect wealth transfer - based on the lottery's odds. But, looked at from this perspective, the question of "should I buy a lottery ticket?" seems like it might be slightly more complicated than "it's a tax on idiots".
But I'm reminded of my current .sig: "Then again, I could be wrong." And even if this is, in fact, a valid viewpoint, it brings up further questions, such as: how can the friction be minimized, and the efficiency of the transfer be maximized? Does deliberately introducing randomness at any point in the process ensure that at least some of your MWI-selves gain a benefit, as opposed to buying a ticket after the numbers have been chosen but before they've been revealed?
How interesting can this idea be made to be?