The question of bringing a gift to the wedding has no universal answer. It varies from tradition to tradition, and even depends on the destination of the wedding.
In some cultures, guests ought to bring a wedding gift along with them. The weddings in these traditions take place in the premises of the home, and there is usually a heavily laden table specially designated for wedding gifts.
In such cases, when the other people around you are bringing wedding gifts for the newly married couple, it becomes your moral etiquette to do the same.
Whereas, in other cultures, it is not necessary to bring a gift along with you on the day of the wedding. This can be due to several factors, including the destination of the wedding, that is, the location of the wedding can be such that it becomes inconvenient for the host to carry all the gift items received back to their home.
Another reason can be people in some traditions prefer that the guests do home delivery of the wedding gifts to avoid misplacing of any commodity in the hustle-bustle of the wedding.
To summarize, wedding gifts are a must as it is part of the wedding etiquettes set by society. But the only thing that varies is when and where you are delivering the gift.
Some prefer to bring it along with themselves on the wedding day, whereas others are more inclined towards providing the gift to the home of the groom and bride within a few months of the wedding.