I was raised as a Roman Catholic in the US. I never encountered what you have described. Perhaps it is a regional variation on RC. I was never taught a cult of saints; I was never taught that they played an intercessionary role between a person and God.
I was taught about the saints, what made them saints, what great examples they gave to us, and to meditate on these examples in order to incorporate that attribute into our own lives and behavior: to become saintlike ourselves.
I think that the living and dead, if they had ties of affection between them while both were alive, continue those ties on past the death of someone. So the living and dead can still take an interest in each other in a loving and healthy way, and help each other. The living can help the dead find peace through prayers directed at the healing of the dead person's weaknesses. The dead can encourage the living.
Three RC priests from my childhood saved my life and helped shape me into the person I am, even 50 years later. I have a real soft spot in my heart for people of any stripe who dedicate their lives to helping others. They are the real saints.
Although I neither believe nor disbelieve in "life after death", I somewhat feel the same.
I have met some wonderful beings in my life. I've also been privileged enough to encounter the teachings of long deceased "sages" ( that's how I see them). And sometimes strange things happen which incline me to think that there are deep bonds between the "living" and ... something else, perhaps the "dead", whatever that means, if by the way that means anything at all. So I like to think that beyond life and death, there are some invisible links between beings, and perhaps, between everything ... After all, what would we "be" without the rest of the world, without parents, teachers, friends, foes, and food !? It is only justice to aknowledge that whatever "dies" doesn't completely disappear. And it is healthy to honour what has made what we are possible. But forgive me. I am speaking gibberish.
Now, regarding the cult of saints as intercessors in Catholicism, I must admit that this is a trend which has significantly declined in most areas of the world since the Middle Ages. So I am not surprised to hear that it isn't a strong feature in US Catholicism.
Protestantism being historically strong in the USA and rather hostile to the cult of saints it might not have helped this tradition to flourish there, either.
However it was really a thing in Antiquity and the Middle Ages, in Europe. This explains why pilgrimages were so important then.
Originally, most local pilgrimages were indeed aimed at visiting the relics of a saint, in order to request his help to solve a problem (usually a health problem). According to the Church, the saint could help because he had direct access to God. So the pilgrims would ask for his "intercession", to get some relief from their pains.
The first Christian cemeteries were also probably influenced by this logic. If you visit the catacombs of Syracuse or Napoli, you'll notice that the first Christian tombs usually gathered around the tomb of a saint. According to the historians I've met there. It was a way for the recently deceased, to benefit from the patronage of their saintly neighbour, thus securing a better afterlife. "Intercession".
The same thing applies to the Virgin Mary. I vaguely remember some religious texts still in vogue among the "traditionalist" Catholics in France, where it is explicitly said that Jesus could only be reached through the intercession of his beloved mother. I don't remember if they got this from the Bible (this is doubtful) or from the revelations of some 19th century visionaries (in France, the 19th century saw a major upsurge of ladies having "visions" of Jesus or Mary. Most of the time, these visions had political overtones, because of the recent French Revolution, and the later Commune de Paris).
In any case, this gave rise to a saying mocking this principle of "intercession".
In French : "Mieux vaut s'adresser à Dieu qu'à ses saints". Which means "Better ask God (the boss) than his subordinates (in order to get some results). I don't know if you have the same saying in English. Probably ...