Hmm...ideally. But that's not the reality as far as I have ever seen. You always end up with some vinyl hoses involved, brass valves, aluminium pots, etc...
When I put together my current setup, I did spring for stainless ball valves which are a lot more expensive than brass. I really don't think brass causes harm as long as you don't scratch it up, but stainless is more ideal for sure.
It's tough to avoid plastic tubing unless you are handy with the soldering iron and build an entirely copper plumbing system. Sounds tough to me. I'm always moving things around, and the flexibility of the plastic tubing is very handy.
Aluminium is a hotly debated topic. Is it safe or does it cause alzheimers? Well, I've definitely brewed in aluminium, but I do prefer my stainless kegs. I don't think I have alzheimers...
So, I guess, yes is the answer to your question, but I imagine that achieving that goal will be tough. And it's still worth brewing even if you don't have a stainless/copper system throughout.
Oh don't give me none more of that Old Janx Spirit
No, don't you give me none more of that Old Janx Spirit
For my head will fly, my tongue will lie, my eyes will fry and I may die
Won't you pour me one more of that sinful Old Janx Spirit