It's not that people get annoyed because others are doing things differently. They get annoyed because cash requests can easily make someone feel like they are only being invited to boost the wedding profit. Or it can make them feel like their contribution is being scrutinised.
Especially if it's an evening invite, or you know that having you as a guest hasn't cost much. It's fine for it not to cost much to have a wedding, just don't have a budget wedding (or a big wedding) and then behave like you are charging entry.
A gift is not freely given if its been asked for, and you will never know if a guest really wanted to get you something else, but was made to feel uncomfortable about their cheap and personal gift so felt pressured into giving money instead.
Asking for money removes people's freedom to shop for bargains and get get the best value they can.
Presents should be about the recipient and what they want, but it is also a pleasure to give. I wouldn't want to take that pleasure away from my guests, especially if they have travelled and are paying for accommodation, new outfit, drinks, whatever.