The rise of therapy coincides with two different social changes on both the micro and macro social scales.
People are more insular these days. We socialize less than we did, live in smaller family groups, and move so frequently that we leave behind friends and family to seek greener pastures. There is little sense of community in most places, people don't know each other as they did and the result is a distinct loss of social support structure. For ages and ages people were born, lived, and died in the same places, knowing the same people from cradle to grave. They lived in families with aunts, uncles, grandparents, in-laws, all under the same roof. You could talk to people, rely on them to help you, give you advice, and support you when times were difficult. Now we don't have that.
The second issue is that the social structure has radically changed. Where before etiquette was a standard-bearer of expected behavior, it has now largely gone away. We are freer to be who we want to be. When I talk about etiquette I'm not talking about Emily Post here. I'm talking about expected social behaviors that define our roles within group structures of any society. You want to see what misery was without therapy, just open Anna Karenina or Madame Bovary. Villages could have their idiots, but the great majority of the social class structure didn't permit deviance so such thoughts and feelings that might arise which were contrary to the society were repressed. You simply didn't have the luxury of having troubles that could not be supported by friends, family, or clergy. Didn't mean they weren't there, just that they had to be buried. Want to know what true mental illness was back when? Just open Jane Eyre. Every character has more issues than National Geographic.
Therapy does for us what religion used to in our post-existentialist society. With no one to pray to, we're left alone with spiritual ennui. We have few family to turn to, friends we don't live, eat, work, and know our entire lives at hand. Therapy and therapists are the western answer; science to the rescue! Whether it's better or worse than what came before, I don't know. In some cases I think it does, but not all. The more I learn about how shamanistic and religious practices work psychologically, the more I realize how important it is for the mind to believe that relief will come in order to make relief happen. Now I'm not sure waving maracas over someone will cure cancer, but if that person believes that their depression, their demons or evil spirits will be relieved by the ceremony, then it may create profound changes in the mind for the positive, just as the devoutly believing may find prayer capable of the same.
Until western society moves away from Renaissance/Enlightenment/Existentialist culture, I don't think we can find an adequate replacement for therapy.