Why? What's wrong with the standard behavior?
If you use a provider like gmail or hotmail, there's a chance they're not set up as your mailto link handler. So in that case, some random email client you have installed will open up and bug you with its first time setup wizard.
Best case, the user is annoyed but still manages to copy the address manually. Worst case, they conclude the link is broken and don't use it.
so, they should set themself up. what drives someone into invent yet another tool which accomplish something on a much higher cost, which is other programms' responsibility and those could less painstakingly fix it.
But at the same time it's not easy to explain to a client that their email link might not work for a sizable portion of their visitors, especially if they've seen solutions that work all the time.
I also agree about avoiding unnecessary bloat and this seems like a decent tradeoff. It's just a tiny popup that includes the native option, so you could argue it sits between a plain mailto: link and a full-on contact form with a backend service for sending emails/texts.
The advantage with the standard is that my phone proposes from itself what it would do when I click a "tel:" URL or "mailto:" URL. And what I do most is just long-press and copy to clipoard. As this uses the native UI from my mobile OS, this just feels better then a HTML-rendered custom UI.
This is one of the old and golden web rules: Don't surpise the user with some UI he would not expect. Be consistent to the standards.