That's what I still do, use an oversized ground sheet and simply pull it over you when needed. maybe not ideal, but it works well enough for me, especially on summer trips. I've also been known to use my rain jacket and/or propped up backpack to close up the opening in a tarp, or of course just spread my rain jacket over the sleeping bag, etc...
The trouble with using a poncho for a ground cloth is it isn't going to last long. Ground cloth duty is very hard on ponchos.
Back in the day ( Circa 1975 –onward ) all I often took with me was a G.I poncho.
It was my ground cloth, rain gear, and I often wrapped it over my bag and closed it, bivy style, with the snaps along the edge.
Trouble was, if I used it for rain gear it was soaked by the time I needed it to sleep in/on it, ( not good! ) and holes would develop in a single summers use. ( also not good. ).
Circa 1985 I picked up then-state-of-the-art second generation gore tex rain suit, and started carrying a "sportsmans blanket" ( similar to the "casualty blankets" used in the military ) for a ground cloth. Then the G.I poncho was used only as my shelter, and I got pretty adept at cobbling together a dry haven for the night using everything I had with me.
Then I realized how heavy it all was – ( G.I poncho, sportsmans blanket, rain suit, ) and how small it really is, and that it was still really only a very minimal shelter setup, so I started carry bigger poly tarps, and finally in 1993 I broke down and bought my first tent. But I still used tarps for summer trips.
Now I’m devolving again back toward tarps and ground sheets. Go figure…
But I figure rain suits are now so light and cheap that I find I always pack one even if rain isn’t expected ( my current is Dri-Ducks, 10.1 ounces for a medium sized suit ), and a downright huge polycro ground sheet is silly light. I’ve been meaning to add tape tie-outs to the corners of my polycro tarp. ( I love what David has been doing with his polycro tarps! )
Add a decent sized tarp and you should be fine, especially for summer trips.