In particular, taking the "number of possible universes" seems problematic to me, as we can only obverse the one in which we interact. And even taking that for granted, what is so astonishing that the actual one is the one that is compatible with our existence? I mean, if any possible universe could have happened, then the one we live in had actually an equal chance to exist with any other. Since this perspective assume that at least one universe must actualize, then pure randomness by drawing of lots is enough to explain the result. No need for a teleological purpose. Apply Law of Parsimony and you are done: Anthropic principle add needless ad hoc assumptions to reach its predetermined conclusions, especially in its strong version.
Also, the anthropic principle stands on many assumptions, including that the simulated models of tweaked universes do reflect other conceivable world in a fiddle manner would they be actual things.
It also neglects that among an infinity of variation, you surely should be able to come with totally different forms of "life". That is, for example it takes life as a carbon based structure, so you need universes with constant tweaked for enabling star to produce and disseminate carbon before they collapse. But on the counterpart, it can't pretend if you take it seriously, that other universes could not have produced very different form of "life". To my mind, we have no idea if our current actual universe is not also populated with non-carbon based life form.
Also this kind of theory emphases greatly on what the world did allowed with these tweaking. But, among an infinity of other combinations, who would seriously consider that nothing better could have been produced than a mankind tormented in wars and questions which are at best extremely hard to solve for its limited cognitive abilities, if not definitely out of its reach?
