I think this is a very interesting question, and any attempt at an answer will probably be frustrated by the lack of surviving evidence. It's true that the Greeks were a very sporting people; so much so that they quite literally set their clocks by it. The four year Olympiad, coupled with other lesser Panhellenic games, gave structure to their reckoning of years in much the same way that the Romans used Consulships, the English used reigns, and we use decades.
Tertullian, in his contemptible joy and relish upon imagining the fate of the damned in hell, derides various mainstays of Classical culture;
QuoteHow vast a spectacle then bursts upon the eye! What there excites my admiration? what my derision? Which sight gives me joy? which rouses me to exultation?--as I see so many illustrious monarchs, whose reception into the heavens was publicly announced, groaning now in the lowest darkness with great Jove himself, and those, too, who bore witness of their exultation; governors of provinces, too, who persecuted the Christian name, in fires more fierce than those with which in the days of their pride they raged against the followers of Christ. What world's wise men besides, the very philosophers, in fact, who taught their followers that God had no concern in ought that is sublunary, and were wont to assure them that either they had no souls, or that they would never return to the bodies which at death they had left, now covered with shame before the poor deluded ones, as one fire consumes them! Poets also, trembling not before the judgment-seat of Rhadamanthus or Minos, but of the unexpected Christ! I shall have a better opportunity then of hearing the tragedians, louder-voiced in their own calamity; of viewing the [comic] play-actors, much more "dissolute" in the dissolving flame; of looking upon the charioteer, all glowing in his chariot of fire; of beholding the wrestlers, not in their gymnasia, but tossing in the fiery billows; unless even then I shall not care to attend to such ministers of sin, in my eager wish rather to fix a gaze insatiable on those whose fury vented itself against the Lord. (De Spectaculis, Chapter XXX)
This from the group that claims to have 'built Western civilization'.
Among the classes of people condemned by Tertullian, there were, of course, people who took to more than one discipline. Cleanthes, successor to Zeno, was a wrestler before he turned philosopher. Socrates, in an often paraphrased quotation from Xenophon's Memorabilia, had this to say;
QuoteIt is a base thing for a man to wax old in careless self-neglect before he has lifted up his eyes and seen what manner of man he was made to be, in the full perfection of bodily strength and beauty. But these glories are withheld from him who is guilty of self-neglect, for they are not wont to blaze forth unbidden.
Lucretius does have Epicurus 'lifting up his eyes', but to a different purpose;
QuoteDisplay MoreHumana ante oculos foede cum vita iaceret
in terris oppressa gravi sub religione,
quae caput a caeli regionibus ostendebat
65horribili super aspectu mortalibus instans,
primum Graius homo mortalis tollere contra
est oculos ausus primusque obsistere contra;
quem neque fama deum nec fulmina nec minitanti
murmure compressit caelum, sed eo magis acrem
70inritat animi virtutem, effringere ut arta
naturae primus portarum claustra cupiret.
QuoteDisplay MoreWhen human life, all too conspicuous,
Lay foully groveling on earth, weighed down
By grim Religion looming from the skies,
Horribly threatening mortal men, a man,
A Greek, first raised his mortal eyes
Bravely against this menace. No report
Of gods, no lightning-flash, no thunder-peal
Made this man cower, but drove him all the more
With passionate manliness of mind and will
To be the first to spring the tight-barred gates
Of Nature’s hold asunder.
I should rather, if I accuse anyone, accuse them of self-neglect who have been inattentive about sharpening their minds, the stakes are so much higher.
Epicurus may have been in ill health for a good part of his life, a sure sign of moral corruption to those who misconstrued man's relationship with nature.
Lucretius does mention bodily strength several times, most notably in Book 5 in his discussion of primitive humans, but there gain he comes back around to the faculty he deems more important;
QuoteKings began to build cities and to found citadels, to be for themselves a stronghold and a refuge; and they parceled out and gave flocks and fields to each man for his beauty or his strength or understanding; for beauty was then of much avail, and strength stood high. Thereafter property was invented and gold found, which easily robbed the strong and beautiful of honor; for, for the most part, however strong men are born, however beautiful their body, they follow the lead of the richer man. Yet if a man would steer his life by true reasoning, it is great riches to a man to live thriftily with calm mind; for never can he lack for a little.
The other side of the story is that people in Lucretius' day were likely far more active than most of us in developed countries today. I have no doubt than many an old bread-kneading and water-carrying granny could put my forearms to shame.
Some day I'll stop quoting Thoreau, but it is not this day;
Quote“If you would get exercise, go in search of the springs of life. Think of a man's swinging dumbbells for his health, when those springs are bubbling up in far-off pastures unsought by him!”
Your mileage may vary.