Why some phones need a 5V charger although the battery needs 3.7V only?

If you look at the charge profile of a lithium battery you'll see that at certain points it changes from constant current to constant voltage charging: -

This means that some form of "in series" charge control mechanism needs to be present to act initially as a constant current source then change to a constant voltage source. This charge control circuit comes with an overhead - it needs maybe 0.5 volts across it (minimum) to do its job.

Given that the final part of the charge regime is constant voltage at usually 4.2 volts, it makes sense to use a wall wart with 5 volts output. Even if the wall wart dropped to 4.7 volts the charge circuit would still have enough overhead to deliver 4.2 volts.

Another reason is standarisation - a few years ago the EU pushed for standarisation of the charging connector in phones which ended being micro USB. USB implies 5V.

And as a personal note I worry about those devices which require over an amp to charge properly charging through USB 2.0.