I remember doing a letter writing campaign regarding Malawi. Back then there was no Internet, no email, no social media, so it kinda made sense. Today, I'm not so sure.
Which lends credence to my theory (and apologies if someone has already mentioned this) - that the letter writing campaign isn't so much to try to convince Russian authorities of anything, but to impress on dubs in the US, and other 'free' countries, that persecution is real, and it could be them next. A side benefit is that it gives them a sense of solidarity, but the the real intent is to give them anxiety, put a sense of dread in their life, hopefully pushing them to come closer to 'mother', not letting the 'world' seduce them or pull them away from their service to the organization.