standard model - Can quarks be considered real and elementary?

In our current theories all hadrons are made up of quarks and gluons.

This view reduces considerably the big family of hadrons by providing a very logical structure in which all quantum properties values of the hadrons are originated from the valence quarks' quantum properties. But since they cannot be observed isolated, in the sense that electrons or positrons can be, the theory assumes color confinement is just part of the game.

However actual calculations of QCD use a view where they are quarks and gluons are distributed in a space-time volume, which is needed to describe much of the rich phenomena of high energy physics.

But all of this makes me wonder:

Are quarks real and elementary? I mean, is there more evidence supporting that they are more than just a model that works?

Since hadronic matter cannot by split into pieces smaller than the smallest hadron, couldn't reality be explained also by a model where all observable hadrons are the elementary ones, which follow rules for transforming into other ones, etc.?

By the way, this last idea was already presented by Hagedorn on his very famous known paper, in the end where he tries to give a phylosofical point of view to his model, so I wonder why was it discarded.

Answer

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.