That’s a good idea and it’s been proposed before.
This particular update to the invite system was almost entirely aesthetic/visual. We decided against making any functional changes to the way it works to avoid running into complications, given the complexity and age of this particular feature. That seems to have worked out pretty well so we are happy with the result! 
I agree we should change it so the invite is created immediately upon clicking the invite link in the sidebar, which would be a big improvement. 
Can’t make any promises about when this will bubble up to the top of the priority list, and the invite system is delicate enough that a change like this cannot be considered pr-welcome.
To share some more context about where we are at with the invitation system… every invite that is created is added to the member’s pending invites list which could become cluttered with invites that are never be used and the member will forget why they created them in the first place and with whom they might have shared them. To address this, maybe we can add a cancel button to the invite popup. If selected, the created invite is deleted, maybe after showing an “Are you sure? Invite will be deleted. Yes No, go back” confirmation message.
Invites eventually move to an expired list where they persist forever unless the member decides to delete them. By default this takes 100 days for links, and occurs immediately when an emailed invite is redeemed.
There’s also a redeemed list but that just shows the users who accepted an invitation and when, but does not reference the specific invite used. That last column could be a link to open/edit the specific invite.
And finally, there is currently no centralized place for admins to see which members are creating invites and how many, and how successful they are at growing the community, and to make configuration changes to suit the particular needs of their community. By default, badges are created to reward members who do alot of inviting, and the person who invited a member is indicated on their member profile.