Taking Many-Worlds seriously is not philosophically free. It generates several deep puzzles that advocates have only partially answered.
The probability problem is the most serious. In ordinary quantum mechanics, the Born rule tells you the probability of each measurement outcome, the probability equals the square of the wave function amplitude. But in Many-Worlds, all outcomes happen. If all outcomes happen, in what sense is there a probability of any particular outcome? What does it even mean to say there's a 70% chance of spin-up, when there will certainly be a version of you that sees spin-up and a version that sees spin-down?
David Deutsch proposed a decision-theoretic derivation of the Born rule: a rational agent who accepts Many-Worlds should, for decision-making purposes, treat the branch weights as probabilities. David Wallace has elaborated this into a rigorous argument. Critics argue this is circular, it assumes a rational structure that already embeds probability-like reasoning. The debate is technically sophisticated and genuinely unresolved.
The personal identity problem is philosophically vexing and slightly vertiginous. When a quantum event branches, which branch are you? If you are about to do an experiment that will cause the universe to branch into two versions of you, is that more like surviving (both branches are you) or more like dying (neither branch is fully continuous with the original you)? This connects directly to Parfit's work on personal identity, and Parfit himself concluded that his analysis of personal identity as psychological continuity was supported by, not threatened by, Many-Worlds.
The ontological extravagance problem: Many-Worlds posits an unimaginably vast, constantly multiplying ensemble of worlds. To many physicists and philosophers, this is not parsimonious, it is reckless. Occam's razor should cut it away. The Many-Worlds advocate's reply: Occam's razor is about the laws being simple, not the entities that follow from those laws. A simple law that generates complex consequences is still parsimonious at the level of the law. The inverse square law of gravity generates an astronomically complex universe of objects; we don't reject gravity for being ontologically extravagant.
The competitor interpretations each have their own costs. The Copenhagen interpretation is pragmatically useful but philosophically evasive. Bohmian mechanics (pilot wave theory) adds hidden variables and requires a preferred reference frame, creating tension with relativity. GRW collapse theories modify the Schrödinger equation itself, adding a physical collapse mechanism that is detectable in principle but not yet detected. The choice between interpretations is, to a significant extent, a choice between which philosophical problems you find least intolerable.
What is not in dispute: something deeply strange is true about quantum mechanics, and our ordinary intuitions about reality, identity, and probability require significant revision in light of it. The Many-Worlds Interpretation forces this revision more directly and honestly than most alternatives.