The things with tropes is that they need to keep being supported by other tropes down the line. Nisekoi (Onodera; share red scarf, share umbrella, childhood promise), Bleach (Rukia; first girl, red string) had all sorts of flags but ultimetly when elsewhere after the tropes died down one character and went to someone else.
First girl is just one trope and it can mean 2 things. The first girl introduced in the story, or the first girl introduced to the main character that he didn't know before the story began. Hina fits the first while Rui fits the second.
Since, Hina has had the 'in sync' trope, the 'first kiss' trope, the 'visual couple' trope (when people suspect they're a couple just by looking at them) the 'proposal' trope (ring and all), the 'bath hotel' trope, the 'love fireworks' trope (twice), the 'self sacrifice for love' (hina's job, her relationship with Natsuo among other things) trope, the 'die for love' trope (though thats iffy since he lived and was with Rui), the 'devotion' trope and 'always love'.
Rui has the 'first time' trope (sex), the 'jealousy' trope (for both of them when Alex and Momo were involved), the 'high school roof' trope (though Hina almost had that, only Rui got confessed to on it), the 'commitment' trope (exchange watches which she gave back).
But she has as many negative tropes as positive. such as 'Jealousy', 'easy to upset', 'Trust issues', 'in the way of true love' (though suspect until its actually confirmed), "doomed to fail" (long distance, as well as their issues with each other), 'break up' among others.
Hina pulls ahead on good tropes since her only bad ones are 'alcohol', 'doomed to fail' (only because of outside circumstances which are now gone)', 'illicit relationship'(which is over) and 'love from afar' (because of Rui, which is now over).
tldr: Tropes need constant backing to actually mean anything and the good must outweigh the bad. Hina has more good than bad, Rui had more bad than good.