-needs a save feature.

There is a save feature for single-player games.

To save a game-

While it's active, click on the "Saved Games" link in the secondary menu (right below where "Multi-Player"/"Coins"/etc. are- under Active Games, you'll be able to save the game (and load saved games).

Thanks I did not know that was a thing.

^^^ it's not easy to find, and very difficult to remember to use...

game should offer to save at the beginning...

It shouldnt be called saved game but save game.

You can turn auto-save on somewhere too, in the settings I think?

It asks you whether you want to auto save when saving a game.