I feel it has to do with how Hashirama never really chose Madara over everything else the way Naruto did and Zabuza eventually did as well.
When it comes to Zabuza and Haku we see them die for each other in a way that reminds me of samurai tales of lovers that'd kill & sacrifice their lives for each other.
For example, in the tale "Implicated by his diamond crest" after a man called Buzaemon kills Daiemon, lover of Tannosuke, Tannosuke swears revenge on Buzaemon and kills him in a duel but he also dies in the process, his remains were buried in Daiemon's tomb.
or the tale "The Boy who Sacrificed His Life" where Senjuro saves his lover, Sazen, from being killed by the enemy, a man called Rokunoshin, and instead he himself is the one that receives a deadly wound in place of Sazen.
Sazen finds out about this and decides to kill himself as well.
Haku & Zabuza's story feels like a mix of both tales, I don't know for certain if Kishimoto read these two stories specifically or if he just read a bunch of samurai homosexual love stories and combined the tropes in them for his own work, but the influence is there. Kishimoto has Haku sacrifice himself for Zabuza & Zabuza ends up fighting a bunch of ninjas to the death, both laying next to each other.
As for Naruto and Sasuke we see Kishimoto use half of the existing shinjuu tropes: a vow of double suicide, the tattoos (traditionally you'd get a tattoo of your lover's name on but Kishimoto decided on the sun & moon tattoos instead) and mutilation. Each one demonstrating a higher level of devotion between the lovers.
When it comes to Madara and Hashirama we do get a scene of Hashirama willing to kill himself to prove his sincerity to Madara in a scene that looks similar to a seppuku ceremony, which is also seen in homosexual samurai stories, but that's where their demonstrations of devotion begin and end.
So to me, the fact that Hashirama is on his knees rather than laying & dying next to Madara like the other two is Kishimoto telling us he's not as devoted to Madara the way Naruto is to Sasuke and Zabuza to Haku.
It's also not lost on me that both Zabuza and Naruto long for an afterlife with Haku and Sasuke respectively, with Naruto wondering if he's in heaven and Zabuza wishing to go to the same place as Haku after his death.
This is also an extremely common trope in Edo Japan literature where ill-fated lovers seeked paradise after death.
But Hashirama never expresses this desire during their final conversation, all he does in the end is say he'd like to share some drinks as war buddies/comrades with Madara right as they're dying. It serves to show that Naruto and Sasuke's bond is much deeper than the one of their predecessors but it's still sad nonetheless.
So I'd argue is Kishimoto using the characters physical language to reassert this sort of "distance" between them that doesn't exist for the other two pairs.