As far as I see it in the video, you first get the popup to enter the parameters. If you finished entering them, you have the finished blueprint in hand and can place it. My guess is that this is a regular volatile blueprint now, like the one you get if you copied but not yet pasted something. This is an item you're able to put into your inventory instead of placing it, and voilà, there you have your regular blueprint you can place a hundred times.
Or may be (and that would be my version of your feature request), the last placed parameterized blueprint is pushed onto the copy+paste stack and you could recall it with CTRL-V.