Chess armageddon

A match of an unlimited number of games, but with a time limit for the total time of all moves of the match for each player. For example, if a game ends with players having 2 minutes and 1 minute remaining on their clocks, the next game begins with the clocks set to that time remaining.

A match ends if one player leads by (say) two points, or if one player loses on time. There is guaranteed to eventually be a result.

This method seems superior to the current "white must win" Armageddon tiebreak method because it avoids the white-black asymmetry.

Another idea (by someone else) is to have geometrically decreasing amounts of time for successive games. This is elegant because the geometric series converges, so the match is guaranteed to take finite time.