Ah, but the customer does not know everything they want, due to the fractal nature of reality. The closer you get to the end product, the more detail is resolved, and more work is added.
Xeno's paradox [0] doesn't apply here. Some projects do actually finish.
[0] https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_an...
Your time estimates should always include time for research and design. The customer can sign off on what you're about to write at the end of that (whereas beforehand you give them a wild ballpark figure made by senior devs - not management!)
You're right, design is very very necessary and should be given plenty of time. But it's not a magic bullet.
If they want the liberty to "change their mind on the fly" then they should buy man-days which is a completely other thing. Or, they can buy supplementary mandays for whatever they want at the daily rate without changing the contract, or, they can just wait to finish this contract and start another one.