What is the reason for cards stating "Until end of turn, you don't lose this mana as steps and phases end"?
In the Comprehensive Rules it says (emphasis mine):


  106.4. When an effect instructs a player to add mana, that mana goes into a player’s mana pool. From there, it can be used to pay costs immediately, or it can stay in the player’s mana pool as unspent mana. Each player’s mana pool empties at the end of each step and phase, and the player is said to lose this mana. Cards with abilities that produce mana or refer to unspent mana have received errata in the Oracle™ card reference to no longer explicitly refer to the mana pool.


So normally you do not keep mana across phases. Thus, for a card like Llanowar Elves, if you use its ability to tap and produce (G), but do not use it on that step, then it will vanish and you will have tapped it for no reason.