I cant imagine you have kids. You can praise a child for failing as much as you want, they are never going to want to only fail. Our child has a deep fear of failure that has prevented them from moving forward with learning particular skills - to some extent it is definitely my own fault as a father as they were able to sense, no matter how much I tried to hide it, my inner dissatisfaction with some of this failure (VERY subtle, hidden, merely the lack of my positivity at their failure was all they needed to perceive to develop a pretty significant and demotivating fear of failure). So we are actually having to tell our child, "please go and try, and fail. we WANT you to fail. because if you aren't failing, you aren't even trying. So please feel free to FAIL as often as you need. the more you fail, the more you are trying". We are about as close to what you are describing as "rewarding for failure". To think that this means the kid is going to intentionally do poorly on things, well, that's not our kid and not any kid I've ever known, so what you are referring towards sounds like some kind of theoretical thought experiment with no basis in reality, and definitely something that would very easily lead kids like mine to be petrified of trying anything.
my personal experience as a parent directly matches the point of view of this article, which refers to research from child development experts.
> Our child has a deep fear of failure that has prevented them from moving forward with learning particular skills
What I am saying is actually in-line with your approach of encouraging them to overcome that fear. My disagreement is when you tell them failure is ok. You are confusing "try+fail" with "try". You praise their perseverance not their failure and perseverance isn't possible because you fear failure, it is possible because you believe in them and love them no matter what, their worth isn't tied to the outcome of their efforts, they persevere because they want to succeed and because failure sucks.
To put it differently, when you say "it's ok to fail" you want them to not feel bad about themselves when they fail. But the shortcoming there is you didn't tell them failure itself isn't good, it just doesn't define them and shouldn't be feared.
In the real world they will fail a lot and you won't be there to coddle them. The best you can do is teach them to not fear failure or be discouraged by it but to understand its cause and overcome it. To despise failure without making it your identity and celebrate and pursue success.
Last thing, if praising means showing love and affection then that is just messed up, that's a given! You should display affection to a child no matter what, not contingent on their success or failure. I am sure you agree with me on this, but also, that means reaffirming to them that their value and worth in life is also not contingent on their success. But nevertheless, success should be pursued and failure despised because failure in the long run means harming themselves or harming others one way or the other. Failing at math isn't a big deal but accepting failure there could mean a mindset that accepts failure in their jobs, marriage, friendships, business,etc... and expecting others to praise them when they fail and getting upset when that doesn't happen.
my personal experience as a parent directly matches the point of view of this article, which refers to research from child development experts.