Unless you have a prenuptial agreement that manages to cover every possible future (and often even then), the longest and hardest part of any divorce is dividing the property fairly between the two spouses. Not every family has a million dollars in assets or owns half a dozen businesses, but fairly dividing the assets is just as important (if not more so) for families without a lot of money. After all, when there's less money to go around, it's that much more important that it go to the person who deserves and needs it.
Of course, most families don't keep all their net worth in an easily divided savings account. Families own houses, furniture, home electronics, cars, stocks, bonds, IRAs, and much more. You could sell everything, convert it all into cash, and divide the pile evenly and it still wouldn't be fair thanks to the way assets grow and shrink in value over time.