I think it's possible, but the current trend is that by the time you can run x level at home, they have 10-100x in the frontier models, so if you can run today's Claude.ai at home, then software engineering as a career is already over.
My poorly informed hope is that that we can have mixture of experts with highly tuned models on areas of focus. If I'm coding in language Foo, I only care about a model that understands Foo and its ecosystem. I imagine that should be self-hostable now.
You can run quite powerful models at home on a maxed out Mac Studio. The difference between those and SoTA is more like 2x.