right behind you

once a servant, always a follower

Izuru Kira is currently at the top of my "most pitiful Shinigami" rankings chart, though without a negative connotation. In the case of HitsuHina, Kira is a victim from all sides: not only is he hurt and/or rejected at most places he's gone to (Almost frozen to death by Hyourinmaru? Completely useless in front of Haineko? Just name it), he is often used as a faithful puppet by the hands of evil.

A shy but determined admirer of Hinamori's since school days, Kira can hardly be called a supporter of Hitsugaya and Hinamori's relationship from whichever way. Even if we eliminate all romantic factors from Hitsugaya's system, the little captain shall remain an unavoidable obstacle on Kira's way as Hinamori's one and only guardian figure. Furthermore, Kira is extremely loyal to Soul Society's class divisions: he would never talk back to anyone his senior under whatever circumstance, thus making it easier for Hitsugaya to stand up against him when needed.

In my opinion, Kira and Hinamori are too similar in nature to be practical suiters. Let's take up the Aizen-Gin case as an example: judging from Kira's personality, he would have stopped Hinamori from attacking "Captain" Hitsugaya while preventing her from being hurt. However, he didn't take any action because of Gin's presence: to Kira, commands from his captain are absolute and must be carried out at all cost. The same goes to Hinamori: she would hold onto her faith in Aizen even after she's been stabbed to death by the same person. Because both Kira and Hinamori are born to be followers, there'd be nobody to lead the relationship if they were ever placed as partners: Hitsugaya and Gin (or even Aizen) would definitely do a better job.

In conclusion, Kira is an indirect stimulant to Hitsugaya and Hinamori's relationship: his presence is a soothing relief for the most angsty HitsuHina moments, so to speak. What a poor guy.