Recipients are set per alert, not per store, so the people who care about low stock do not have to be the people who care about overdue purchase orders.
Email is the one channel that cannot send a message per alert. On a large catalogue that would be thousands of emails, which costs both deliverability and money, so email alerts are always grouped into a summary: daily, weekly or monthly, at a time you choose.Picking Email on an alert that was sending individually moves it to a daily summary rather than leaving a combination that cannot be saved.
Every alert email carries an unsubscribe link. Using it removes that one address from that one alert and leaves your other alerts alone.If it was the only recipient, the alert is switched off rather than left running with nowhere to send. A rule that looks active but can never deliver is worse than one that plainly says it is off.