Neat idea. This probably has the disadvantage of coupling deployment to a service. For example how do you scale up or red/green (you'd need the thing that does this to be aware of the push).

Edit: that thing exists it is uncloud. Just found out!

That said it's a tradeoff. If you are small, have one Hetzner VM and are happy with simplicity (and don't mind building images locally) it is great.