Can quarks be considered real and elementary?

As mentioned in the OP quarks vastly simplify the theory of hadrons, like atoms did chemistry, and despite confinement Rutherford-like experiments were performed for them too, by Friedman, Kendall and Taylor who received the Nobel prize for it in 1990: "unexpectedly large numbers of electrons being scattered at large angles provided clear evidence for the pointlike constituents within nucleons. These constituents are now understood to be quarks."

But can quarks still be considered non-existent? Technically, yes. This is the answer Mach gave about atoms in the 19th century: they are just fictions, and the theory can be re-arranged in a way that eliminates them, e.g. by connecting only measurable quantities to each other, and purely mathematically (Mach and a leading chemist Ostwald even refused to mention atoms in their works after 1870). This remained true even after Rutherford's experiments, and it remains true today despite the technology that (ostensibly) "allows them to be imaged, split and smashed". Indeed, one can even eliminate everyday objects and reduce everything to sensations, as some positivists suggested. But doing so will make for a very unattractive theory.

Of course, it can also go the other way: at the end of 19th century the ether was a solid element of reality. Some even expected a theory of everything out of it, like Michelson in 1902, see Kragh's Quantum Generations, p. 4:

"The day seems not far distant when the converging lines from many apparently remote regions of thought will meet... Then the nature of the atoms, and the forces called into play in their chemical union... the explanation of cohesion, elasticity, and gravitation — all these will be marshaled into a single compact and consistent body of scientific knowledge... one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substance — the ether."

And then the ether was no more. But that does not happen very often.

What you propose is called nuclear democracy, and was very popular in the days before the standard model emerged. See also the discussion in http://www.physicsoverflow.org/22971 , where you can read about (among others) my present view of it.