You can be paid/coerced to vote for someone even if there's total secrecy. For example, you can take your cellphone in and take a picture of your filled out ballot to collect a payment.
Unless you want to start the confiscation of cellphones before voting in person, the risk of a coerced or bought vote will always exist.
[1]https://www.perfil.com/noticias/politica/elecciones-2025-de-...
And then you can go up to the election workers and tell them you have a spoiled ballot and want a new one, which they have to give you. That's one reason such schemes don't work right now.
Source: I volunteer as an election worker every year in Iowa.
I mean, compare the number of people who've flown over Barbara Streisand's property to take a picture of her house to the number of people who had a copy of said picture in their browser cache.
You can read more about this peculiar scaling factor of the internet in Bill Gates 1995 book The Road Ahead.