You're absolutely right. The 4th house is the deepest house, it symbolizes the connection with the clan, with the family, with the roots. But there is a small remark here - if Mercury is in the fourth house, there will not be such a strong attachment to one's roots, to the family, to the land, of course, if there are no other indications. For example, the Sun and the Moon in the 4th house will certainly give a strong heartfelt attachment. But if the 4th house is more light and there is only Mercury there, the connection will be manifested more at the mental level - to talk, read, discuss something. This is also one of the indications of moving away from one's native land. In this case, the person, not clinging to the roots, runs to where it is interesting. Very easy to take off.
It is often the case that a person was born into an intellectual family. Parents are educated people, they can be scientists. And they will invest in the education of their child.
In the house of such a person, there are many books and conversations on various topics. It may be an indication of home schooling. There may also be regular meetings, frequent visits of relatives, friends, gatherings of some interest groups in the house.
Mercury in the 4th house gives figurative, beautiful thinking, good imagination. Such people often become good storytellers, as they are wonderfully able to compose and write.