What you're talking about is referred to as triggers (or events) and while marketers have done this for decades, it's only been self-service in email for a few years.
I've seen some basic triggers enter into lower end providers but probably not enough to do it all through the provider the easy way. Under this method you share your customer data (ecommerce, crm, contact, analytics, etc) with the email provider through an ongoing feed passing over whatever fields are needed (name, email, order history, order date, etc) then build campaigns with a "Drag and Drop" style approach.
The difficulty here is data syncing. The vendor has to take enough info points in (and you have to have some sort of data warehouse to send them from) to be able to key into the segments.
There is of course the hard way which any provider with a decent API supports.... Here you would create a script on your ecommerce platform to identify each different type of email and on a daily basis (or such) trigger a request to the email vendor to send a pre-defined, but otherwise static, message out to someone one at a time looping through each match on each campaign.
While the hard way does require more development and gives you less flexibility, you don't have to worry about syncing data and you do get complete control.
Popular vendors -
If you're doing significant sends feel free to drop me a PM for some industry contacts / vendor names who work at that level.
Btw, your approach is awsome. Be there when it's relevant with a relevant message, not every tuesday because it's tuesday.