Add an API server to the internet bridge (even if it requires newer, more powerful hardware) that supports controlling devices within the local network. Philips Hue provide a great example of how it can be achieved.
My justification is twofold.
Firstly, a local API can be accessed in the event of my internet going down. Ideally the app would be able to detect the internet bridge using something like mDNS. Alternatively its IP can be specified or its "last known" private IP used - this would not be perfect in most cases, but gives options.
Secondly, my main concern when it comes to large investments in smart home is longevity. I do not want to have to shell out for a new heating system anywhere near the frequency I do for a new phone (or even TV or laptop). At some point maintaining support for old hardware will become problematic for Tado - just look at what is currently going on with Sonos and they've been relatively kind in the longevity of their support. A local API would allow owners to continue to use their products in the event that cloud support ends. It would have reduced functionality, but I as the owner would still be able to make the call as to whether I feel it worthwhile to re-invest - and create a whole load more e-waste in the process.