Listening to the extraordinary beauty of their recent duo album Jasmine made up entirely of melodies of lovesongs from the Great American Songbook, you begin to understand why.
As I listened to them I wondered how much these two elderly men from the US, as they played these tunes with such immensely moving sonic romanticism, were remembering the notes of their youth when Haden was thudding out his tribute album Che all through his pulsating bass or the struggling days of 1970 when he assembled and recorded his first Liberation Music Orchestra album.
Or when Jarrett, alongside vibist Gary Burton and bassist Steve Swallow, punched out Como en Vietnam at the apex of US imperialist aggression.
The truth is of course that there is no contradiction here and both musicians are fired by a romanticism which has always been part of the real world.
Jarrett asserts in his sleeve message that "this is spontaneous music made on the spot without any preparation save our dedication throughout our lives that we won't accept a substitute - it's either the real thing or it's nothing. It's either real life or it's a cartoon."
The same real life of hope, love, betrayal and disappointment that shoots through the many albums of Jarrett's Standards Trio, or the quizzical dreams of life and love in Haden's Quartet West albums like Haunted Heart or Always Say Goodbye.
A duo of old men. Perhaps there is bound to be something of a valedictory mood - it includes Goodbye - and it begins with For All We Know, for of course they may not meet again in a recording studio, and this encounter was in the domestic studio in Jarrett's home.
For me it was a coincidence that this album arrived in my home shortly after I had been playing the late '60s albums Life Between the Exit Signs and Somewhere Before, both with Jarrett and Haden in former days.
Listening to its messages in a strange way the sense of continuity overcame all other sensations, as if the exit signs were clearer now and what came before was inevitable in order to create such compelling lucidity of sound now.
For All We Know is played very close to melody with Jarrett's customary chiming, pure notes and Haden's lifelong musical boom, as if he were plucking rope inside the timbered hull of an 18th-century ocean-going ship.
How can they play with such inordinate beauty while still so closely listening to every single note of the other?
The answer lies somewhere very deep inside the intimate comradeship of jazz and the title of the album's second tune, played with such mutual empathy and piercing clarity, Where Can I Go Without You?
The session radiates a curious night-time quality - the jasmine is, of course, a night-blooming flower. But it's certainly broken by a striding version of No Moon At All which cavorts along as if the two men are travelling somewhere fast.
Haden's solo bounces along in twanging joy and Jarrett follows with a jaunty chorus full of heart and optimism.
Not so I'm Gonna Laugh You Right Out Of My Life, which seems to tell a story of love forestalled. Jarrett pulls back on his notes as if the brakes have been tightened on something very precious.
Body and Soul has had legendary status among jazz musicians ever since Coleman Hawkins's tenor saxophone rhapsody of 1939.
Jarrett sounds almost Monkish, like Thelonius turning unforeseen corners and angling his notes inside a body politic full of surprises which provoke a soulful sack of sudden responses.
Haden adds the inexorable heartbeat, beating like life itself. It finishes almost like a lullaby, but a lullaby sung to time-worn adults which continues right through the last two tunes full of a sense of painful transience, Goodbye and Don't Ever Leave Me.
The last words go to the enigmatic Jarrett who can make melody sound simultaneously like both the beginning and the end of beauty.
In his sleeve-notes he writes of the "melting, trans-figurative moment, that feeling of everything being there, just for an instant ... that leads us on to the next pregnant second."
There are 63 times 60 such seconds of Jasmine, all carrying intense moments of reflective and shuddering life, played by two musicians who provoke 140 years of often astonishing artistry and whose union proves how making music together draws in the world to their brilliance.