Good idea, although it doesn't work too well at chess. This concept works extremely well in Go, where normal practice is that each game is played with a handicap that gives each player an 50% chance. This works over quite a large range of ratings.
Games at odds

These earlier discussions may interest you ...
- handicapping-systems---levelling-the-playing-field
- handicapping-system-for-new-players
- odds-games
- handicapped-games
- removing-pieces-as-a-handicap
and these ones specifically around customised starting positions ...
- custom-position-tournaments
- can-i-start-a-game-with-the-pieces-in-specific-position
- does-anybody-think-this-would-be-fun
- new-games-with-predetermined-set-up
- custom-starting-positions2
While it's easy enough to find opponents of an appropriate level online, playing casually with friends often means large differences in ability. How easy is it to get an idea of relative strength by the odds needed to get closer games?
I've heard somewhere before that each pawn equivalent is worth about 100 Elo points, so a 1300 could have a good game against a 1600 at knight odds, or a 1200 might play a 1700 at rook odds.
I would have thought that this would vary with level, ie. for beginners, odds of a couple of pawns or even a piece would make little difference compared to all the errors during a game, while at a higher level even pawn odds would be decisive. Does this seem close to reality in your experience?