I believe strongly in the right to privacy, but I have to admit, I do not want anyone coming into my country who has beheading videos on their phone. Unless they are a journalist or something, obviously.
Answer: approximately zero
How many terrorists would be deterred by this policy?
Answer: none
How many ordinary people would be more likely to carry out attacks or harbour resentment towards the USA because of policies like these?
Answer: more than 0
Someone who hoards beheading videos is not ordinary and it's perfectly in line with the international norms to be able to exclude undesirable people from entering into a country. E.g. Canada won't let people who have past criminal convictions enter, like a DUI.