Good news! We have now added the invite link to the sidebar on all sites, and selecting it opens the invite popup directly. The link is only shown to people who have permission to invite.
For those sites that prefer not to have the invite link so prominent or want to move it below ... more they can set it up as they see fit by using "Customize this section".
You can also add link to the popup directly from anywhere using the https://yoursite.com/new-invite URL.
Discuss this on our forum.