Mobile app? Now they need to develop that, keep up to date with OS version changes, and far far worse, support end users and their bugs?

And worse of all, worry about Apple and Google's arbitrary rejections?

This seems far more costly than email. Just having one dev keeping those apps going, is likely 20x or more than their email costs per year.

at least for iOS there are no costs associated with using Apple Push Notification Service (APNS) but depending on the way you use it you either need to pay for the infrastructure that sends your notifications to Apple or for a service like OneSignal which does that for you. Not sure what the volume of LE is but I am pretty sure it's a smart move to focus on their core "business" (providing certificates) and let other handle expiration notifications.