Your question is posed mainly from a modern Western/Capitalist perspective where seclusion from economical "responsibilities" for spiritual practice is - to say the least - not encouraged. Also, the West doesn't have a tradition of handing out food to begging monks, in fact, in many countries this practice is illegal. It was very different in Asia before the industrialization.
During the Golden Age of Buddhism in China, the Ch'an (Zen) school actually consisted to a large extent of 行者 (wandering monks), who would travel throughout China, searching for the "right" master, entering into a discussion with the master of every temple they came across. This is still a common and widely accepted practice in many Mahayana traditions.
The mythological monk Bodhidharma, claimed as their founder by several Chinese Buddhist schools, would definitely qualify as a wandering monk, as does the mythological Budai.
Also in the Ch'an tradition, there are a series of drawings called the Ten Oxherding Pictures, the tenth picture is entitled "Return to society":
Barefooted and naked of breast,
I mingle with the people of the world.
My clothes are ragged and dust-laden,
and I am ever blissful.
I use no magic to extend my life;
Now, before me, the dead trees become alive.
As for laypeople, Huineng was a layman, but is considered to be one of the most important Ch'an masters.
