Let me begin by stating the obvious: viewers of your website = finite; people on your email list = finite; users of Google = infinite. With that tidbit of info in mind, selling the concept of letting Google do the heavy lifting of informing the world about your shows needs little more than a soft sell.
Google's new event promotion thingy has a few options for implementation, which is good because, while some require a working knowledge of the gibberish that makes up a modern website, some don't. So let's take a look at the easy version:
Start with a popular band website.
If, like me, you're more into widgets than code, you'll be pleased to hear that you can get the same job done by using a canned widget. This new feature of Google integrates with a few names you've likely heard of, like GigPress and BandPage, but my particular brand of vodka is ReverbNation, which is where I staked my claim.
After you establish a presence, you'll want to look for the schedule widget. It's usually somewhere in your admin control panel. Next to it you'll see some instructions for embedding it on your site. From there, just update your ReverbNation page and you'll see the widget on your site update as well.
Or, the hard way.
If you're more of a coder by nature, perhaps you'll want to use another method. I'll say one thing for it: it saves you from using someone else's platform. ReverbNation and it's contemporaries are all fine and well, but they can also be a bit slimy. So, if you're more of a go-it-alone kinda person, you can install the hooks into your site that will inform Google of the pertinent info. It involves using bits of code with names like JSON-LD, RDFa and microdata. I get exhausted just thinking about it.
Now you wait.
Regardless of widgets or code, the next part has nothing do with you and everything to do with Google. Their all-powerful yet inexplicable system will, before too long, get around to crawling over your website. The next time it does, it will see the code in your schedule for what it is: a list of your upcoming events. From there it'll find its way from your site to those nifty Knowledge Graph panels (great feature, awful name) you see in your search results.
Now, even if you add dates to a website no one sees, and a ReverbNation page no one knows about, you'll still get the warm, fuzzy feeling that comes with knowing every one of the seven billion people on this planet have easy access to the details about your solo acoustic show at Edna's Crab Shack in the heart of downtown Caribou.