I think it's a bit beside the point to debate whether the relationship is problematic or not viewing it through a purely romantic lens. I choose to see it more as a story of two fractured people finding true joy and peace in each other (like platonic soulmates I guess), especially since you never see them do anything like kissing and whatnot. It's a heartbreaking story about human connection and love - what makes life worth it is the bond we can share with another person. Two other short manga which reminds me of this one is "white paper notebook" (less sad) and "my broken mariko" (more sad).
One Room Angel