Would this volunteer organization face any legal trouble?

A friend of mine is thinking of setting up an organization, that will have members of the public volunteer to write anonymous letters of encouragement and hope, so they may be handed out at random to people in need.

They would take letters from the general public that volunteer to write and send mail, then they would take the letter and hand it to someone who could benefit from it. Such as homeless people, old people in homes, prison inmates, and so on.

I have raised legal concerns with my friend, in that they are not actually a registered charity, just an unofficial activist organization.

After having it explained to me better, I am not sure if it would be legal or not.

They would be asking for letters to be mailed to them, with them as the named receiver. In other words, in their terms and conditions, they would claim ownership of all mail delivered.

This will allow them to open the mail, to inspect it and make sure the content is appropriate, before handing it over to a recipient.

They would not ask for, or accept monetary or material gifts or donations, and would have a policy, stating that anyone who sends cash or gifts, will have their mail returned when possible, and donated to an official named charity in the event that returning it were impossible.

They would also reserve the right to make copies of the letter, as well as quote it or use it in parts in magazines, articles and other outlets.

They would reserve the right to destroy letters that are not appropriate, as well as more or less do what they want with all mail at their choice.

Would that be likely to be legal?

(I am just asking for personal opinions, and don’t hold anything anyone says as actual legal advice)