You have to dig for the unsubscribe link at the bottom of the email, navigate the unsubscribe website interface which is always wildly different and sometimes absolutely confusing (possibly on purpose). Then finally you have to hope they honor the request.
I think the screener sounds great. I hate that pretty much all online retailers equate a purchase with "we can send you marketing emails". Having a consistent, up front interface to kill these emails that will always work is very nice.
I haven't had a single legitimate company ignore a firm and strongly worded e-mail or phone call asking to not be contacted again. Plus in Europe we have the GDPR on our side and while it's not actually being enforced, mentioning it is usually enough to raise some eyebrows.