This is why Franky, and Franky alone, is the ‘father’ of the Straw Hat Pirates.
When he was only a small child, he was abandoned on the Grand Line by his parents for being a 'nuisance’. Franky knows what it’s like to be abandoned. Not orphaned–his parents are very likely still out there somewhere–but abandoned, not because his parents died, but because they freaking didn’t want him. Franky knows all too well the loneliness that results, of being small and scared in the big wide world, with no one to turn to.
But he also knows what it’s like to be accepted, to be taken in by someone who became more like 'family’ than those he was actually related to. He knows what it’s like to be given a new sense of hope, to be given direction, to discover that he is not a nuisance at all, that he is actually worth something.
…But then he knows what it’s like to lose that all over again, and by actions he perceives as his own fault, just as he viewed the abandonment by his blood father as his own fault. Losing Tom totally shattered him, so much so that he was willing to forego his lifelong dream of creating ships, the thing that basically defined who he was.
But one thing remained. Foremost to being a shipwright, he wanted to be like Tom. Franky wants to be the father-figure to others that Tom was to him. He wants others to know that they are not hopeless. That they are not a 'nuisance’, that they actually deserve to take up space in the world.
So when he returns to Water 7, he gathers up all the misfits and outcasts, all the 'nuisances’, and gives them a family. He gives them a home, and a purpose to live, so much so that they want the same for him. They want him to revive his dream of being the shipwright aboard the dreamship.
And once he does this, he is every bit the father figure he wanted to be. In Dressrosa, when Luffy hears about Ace’s fruit, Franky is the voice of reason. To Usopp, who’s come from a similar-yet-different situation of parental abandonment, he is the first present father figure in that kid’s life, and helps guide him in their similar areas of interest, in which he is more experienced. He knows when to be serious and when to be silly and can switch between the two without a moments warning, entertaining them with his inventions, not because it makes him happy, but because it makes them happy, and that’s what makes him happy.
Because he doesn’t want others to feel the loneliness he felt as a child. He doesn’t want others to feel as though they’re a waste of space or a nuisance. Because he has lived and breathed with a fully human body and with a cyborg one and knows regardless that just existing is never a crime, and while he’s around, no one is going to feel unwanted or worthless.
While he’s around, no one is going to feel fatherless.