It wouldn't have been that hard to keep track of 150 or so people and if one died, just indicate it on the sheet that had died.
As for what TOS did, VOY was made in the 1990's not the 1960's. Shows like DSN and B5 whilst maybe not trailblazers were part of the shift that was happening towards more serialised shows. VOY leaned more towards episodic, swimming aginst the tide so to speak.
TOS only had 3 main cast members, VOY had what 7/8?