No rigid alignment displayed on the character page does not mean that your actions no longer matter or that characters don't have personality. Companions and other NPC characters still have preferences, and they'll still react to your choices, either favorably or unfavorably.
It means that you can role-play your character instead of role-playing one of nine boxes. If dialogue options are tagged with alignment flags, many people would feel more obliged to pick the one which matched the box they put their character in, even if they would prefer to pick a different option. This would be especially bad for "Neutral" alignments which would feel more strongly a need to ping-pong between different ones.