I was first asked this question 30 years ago by a group of US students on a Summer trip around Europe. I was a cricket umpire in the UK for several years, so I know a fair amount about the game and its history.
The reasons for the acceptance of draws in extended-duration cricket are bound up with the origins of cricket as a game. Cricket as an organized game originated in order to occupy people on Sundays in English towns. According to the Church you were not allowed to work. However, at some point, the church decided that playing sports was OK. So….one of the games that sprung up to pass the time was cricket. This is why, to this day, most Test Matches start at 11.30 am, and complete at 6.30pm for a day’s play. 11.30 was the time at which churchgoers left church after the morning service, and 6.30 pm was the time for Evensong. When you watch an all day cricket match, you are watching, to some extent, a fossilized replay of Sunday in an English town or village.
As for the ideas of winners and losers….the game was originally a time-filler, not a means of keeping score, so who won or lost was relatively unimportant. What is still known as Test Match cricket, where a game lasts for 5 days, still has provision for a draw. Also note that this parallels the game of chess, where a lot of matches end in draws, albeit via a slightly different process. In Test Match cricket a draw occurs when time runs out without one team having a decisive advantage, whereas in chess the players agree on a draw because they both can see that neither of them can gain an advantage.
Having said that, teams take winning VERY seriously. The longest-standing Test Match series of note, the Ashes series between England and Australia, is one of the most keenly-contested series in the world. If England loses, national angst and hand-wringing occurs, and Australians the world over lift their beers in celebration of walloping the “whingeing Poms”. If Australia loses, a LOT of beer is drunk in Australia as they agonize, and England has an attack of quiet, understated satisfaction.
I should note that today, most of the cricket matches played at the top level of the game, especially between countries, are played with a rule system that assures a winner. 20/20, which is now the most popular form of mass market cricket, particularly in India, has rules that guarantee a winner.
