"become willing" is correct and usable in written English.
It can be used to describe when someone changes their attitude or opinion and is now open to the idea or suggestion. For example: After much thought, she eventually became willing to accept the new position at the company.
Hopefully, others will become willing to try and invest in drone technology, Rinaudo and Wyrobek said, after seeing Zipline's technology and its impact in Rwanda.
As everyone is cheered by the improvement in the economic and corporate results, they will become willing to extrapolate it.
Doubtless scientists' experiments with meat substitutes will improve to the degree that we will eventually become willing to eat them.
My concern is that even if madrassa graduates themselves are not becoming terrorists, the graduates may nevertheless become willing supporters of violent extremism.
And if people think that prices will continue to rise, they become willing to spend even more, driving prices still higher, and so on.
The moment in which we truly become willing to end war on Earth we will find a way.
But once you adjust to the current climate and become willing to pivot to a new approach, you will see opportunities that you've never noticed before.
Share prices will fall, so that expected returns rise and investors become willing to buy shares again.
It is our belief that with time as the website becomes more established through development and repeated advertising at key health economics events, teachers will become more familiar with it, engage in the initiative and become willing to share resources.
Simply introducing new foods repeatedly can help children become willing to taste them.
Maybe it is because the media has become willing pawns in that endeavor.
