micropayment channels (https://bitcoinj.github.io/working-with-micropayments), are used between 2 parties to send a lot of micropayments. But here there is only one transaction even small.
Also micropayments may help against spam but not agains cold emailing
You can have a micropayment channel between the user and their email provider, and between email providers.
When User A wants to send an email to User B, he sends a micropayment through one of these channels to his email provider. His email provider in turn sends a micropayment to User B's email provider. User B's email provider sends a micropayment to User B.
So in this way, value can be transferred without any on-chain BTC transactions, zero fees, and instantly.