Not true. If you have design ready before the implementation starts (as you should unless it is very simple) then you are free to implementation things separately. Just have the interface well specified.
This is sad, but my point still holds. Perhaps being honest with oneself about real tasks that need to be done will help. Planning the architecture/feature, doing proof of concept etc. are all valid tasks even if they don't bring immediate business values. If you claim that you can only do business features without doing any exploratory work then you are effectively claiming to have an oracle giving you perfect solutions out of the blue. In which case you should stop whatever you are trying to do and start selling the services of your oracle.
We always do a brainstorming before implementing any serious feature / change. Once we have the initial design business gets involved (if we can get their attention...). The results usually works without needing any drastic changes, which is still better than no planning at all. It does require involvement from a number of parties though.
Design is better when it's informed by implementation, IME. The only complete specification is working code; if you accept something lower-fidelity then it's very easy to miss ambiguities.
Even code have bugs so it's not perfect. Your design can incorporate high level algorithm to be implemented, ins/outs, or whatever else high level constraints are most applicable to your domain.