Well, it is something I am capable of doing. Specifically, wasting enemy actions with the daze status. Like I said, Poisonous Shuriken will not even daze on average 1 extra turn (enemies will only spend .88 of a turn more dazed). Since an enemy can't be dazed for a fraction of a turn, this amounts to some combats where Poisonous Shuriken isn't even better than Precision Dart at all and other combats where it's better by 1 turn. Admittedly, you'll have more of the latter (.88 is closer to 1 than to 0). But still, the point is that what Poisonous Shuriken essentially does is give you slightly more daze.
That's not really the relevant point. You're not doing Bloodroot Poison to do damage, you're doing it to gain control. You're a Striker. You do less damage with Precision Dart than you do with Eldritch Strike. You presumably want to focus fire and kill the thing you hit with either of them - so how long the Daze lasts on your primary target ought to be of very little interest. Either it recovers at the end of its turn or it doesn't - it is still sitting next to you proned and you plan to kill it with the help of your teammates in the next round.
What Poisonous Shuriken does is three things:
It gives you multiple targets to damage and then attack. You charge the opponent you hit with your Assassin bonus damage with an AP. Because you target 3 opponents, odds are really high that you hit someone and therefore do damage and daze them. Odds are better that you roll a critical hit, which applies to your Assassin damage too.
Because you tried to daze 3 opponents, you might very well have 2-3 dazed opponents, one of whom the party tries to focus fire and kill. Which potentially negates an attack or two, but also possibly means one of those opponents is going to fail their saving throw and be dazed for the next round - setting up another kill for you.
It targets multiple opponents by default - yes, it doesn't prone, but you attacking 3 targets a round is ultimately good distributed damage with a hint of striker added on. This is good for popping minions, attacking multiple flyers, etc...seriously, anyone who has access to a 3 target ranged at-will should strongly consider taking it simply because it does that.