I grew up in Japan... Cash is a VERY traditional wedding gift. Guests typically send a gift to the home (physical gift... because it is the height of rudeness for a person to open a gift in the presence of the giver) and then bring cash to the wedding itself. ((Money is also given to children on Children's day... and during other celebrations during the year)).
The Japanese don't do the "Money Dance", but that's a common tradition in some Asian countries.
The Money Dance is also common in some parts of Europe.
Envelopes filled with cash, handed to the bride is very traditional of Italian American wedding, and in some (but not all) parts of Italy itself (Italy is actually a collection of 4 or 5 distinct cultures)... and ditto for Greece.
It's only rude or poor manners in SOME countries (like ours, but not everywhere in ours)... so you're VERY right in thinking that this might be a cultural difference.
In many of the countries where cash is the traditional gift, having the NERVE to go and pick stuff out yourself (registering) is the HEIGHT of rudensss. How DARE someone go pick stuff out that they want and then expect other people to buy it???
Rudeness is what one's mother teaches.... it's FAR from universal.
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I should add... I married an Italian American. Close relatives gave us envelopes with $1000 in it. Close family friends did $500. Friends and more distant relations did $100.
My side split equally between Japanese tradition, and Northern European tradition (I even had a gold and silver coin for my shoes!). And my NYC friends also gave cash.