The four games I played at the Expo on Sunday all came down to the last tile:
1) I was the 4th player, I was beaten by 3rd player by 1 point, the 2nd player by ~5points and 1st player by ~15points. So an extra tile could have changed the results game for me. I can't remember the game exactly, but perhaps finishing a city with a last tile would have positioned me in 2nd.
2) I was the fourth player again - This time I won the game, but with an extra tile my points differential would have increased which would have changed my final rankings after game 4.
3) I was 1st player in this game - I drew second place with the final player (3rd this time). If the 3rd player had an extra tile I would have likely been positioned in last place.
4) I was first player again and drew with the game with the last player (3rd again). In the tournament his points differential meant he ranked above me; however if he had an extra tile he probably would have beaten me.
Obviously, my results may not be statistically significant and perhaps after enough games the 4th player disadvantage is 'averaged-out'. During 2-player games the number of tiles maybe less significant because there are often enough tiles to separate the players' skill. In the four/3 player games I described above it is evident that an extra tile would have made a difference to my final outcome; and I think many of the other games being player throughout the day would have changed too.
From a tournament perspective perhaps allocating points based on position escalates the disadvantage; eg scoring 1 tournament point vs 0 tournament points; because of a single tile.
Just some thoughts:
Games such as Go, recognize 1st player advantage and allocate handicaps. They've had a few hundred years to experiment and perfect it, typically first-player must win by more than 7 points against their equal to declare it a victory for example.
Perhaps 5-player games need to add and remove specific tiles from the deck, but I've got no idea how to start approaching that.
Printing 73 tiles isn't really an issue: It could be achieved by printing 4*(4x4) tile-palettes + a (3x3) tile palette, for example.