It totally makes sense, and it’s all about using the path booleans, especially union and difference. I’m going to assume you’re intermediate at inkscape and gloss a bit.
Make your text, convert it to a path, ungroup it and combine the letter paths into one large path.
Make a rectangle to enclose the top and bottom of your text, and convert it to a path.
Copy and paste that text/rectangle twice to have three copies.
Go to one set, select the rectangle and the text, and select path->difference. (Bottom left)
Go to the other, select the rect and text, path->intersection. (Bottom right)
Align the top half text to the bottom half text. Change the top half to be no fill.
Now align everything using your first copy rectangle. Delete the original text (you only needed it for alignment purposes), and you should be left with your two half-texts and a rectangle.
Select the top half text and rectangle, do path->union.
Done! No open paths or gotchas, it will just work.