Engineers solve problems. Doesn't mean all problems are defined properly. That's why part of the hype around design thinking is about solving the right problem before solving the problem right.
Or was just not done in good faith. Which is why having a culture of openness and honesty and acceptance of failure (to an extent) is important to building an effective engineering culture.
The problem is, due to limited information, it is impossible to know where this equilibrium point is. You still have to just make your best guess.
That reminds me a lot of the days when managers did not want to do proper code testing and coverage because without that they could ship more code. Defining the problem upfront and doing rapid iteration not just on the solution but also problem definition is nowadays more important and effective than just shipping.
There is always, always trade offs involved in engineering. As for which trade offs are acceptable sometimes you have influence over that and sometimes it's out of your hands. Design thinking is a tool that can help but it is not a panacea.
For people that don't work in the field perhaps it's not obvious. A good friend of mine is a PHD chemist who works in research (I work as a Materials Engineer in industry) he is always winding me up about engineers doing a half-assed job. I've always thought that our interactions highlight one the key differences between science and engineering, scientists strive for perfection if you will and engineers want workable...
From experience working for a leading hydrodynamics organisation you don't mess around with nature lightly ok you can do costal defence but you just move the problem around.
Oh and normally its the technician who fixes the "engineers" math :-)
"I wish we didn't have so much water!"
"Your wish is my command: all the water now drains out of the city."
"Wait, I meant..."