The focus on the nuclear family, in American terms, seems to be a product of post-war development and suburban living in the 1950s. And yet even harsh critics of the 1950s mostly focus on the people excluded from or hurt by that lifestyle; atomization and familial loneliness are hardly ever raised as major objections.
(I've certainly seen the isolation of housewives raised, but that's not the same as "the nuclear family" and in fact was largely about a stay-at-home lifestyle.)
So I think you're exactly right here: the nuclear family is at worst one of many changes that enabled social isolation. The actual fact of isolation didn't set in until much later, and it's origin could be equally well blamed on problems from cheap consumer goods (no need to share or borrow) to the decentralization of media (no shared icons like Edward R. Murrow).
A proper treatment of the question would admit that the problem is polygenic and look for shared causes or solutions. But the hot-take approach is to pick one convenient issue and treat it as a singular cause.