As you say in your last paragraph, "If they're not writing down the steps, it's more often that they are demonstrating that they don't have a good enough level of understanding to do this", but that is not the situation addressed by the advice you object to. If they are answering the questions in their heads without understanding how to solve them, the questions would not seem to be a good match to the topic. If they do understand how to solve the problem but don't know how to put it in words, again that is a different problem, possibly in how it has been explained to them.
If you take the question 3x + 1 = 10
And solve it (for example) by trialling x=1, x=2 and x=3, then you are able to answer the question correctly. You may even be able to answer a set of questions correctly.
But, you have not learned the relevant algebra skill to be able to generalise this process.
I had this fight with my son years ago. Algebra is process and algorithms, what he was doing was not Algebra IMO.
This website is a resources for teachers of "gifted and talented" students - but, in my experience, this strategy absolutely will not work in a more general setting.
It's often the case that students aren't writing down the steps because they don't understand what the steps are and don't know how to formulate the steps as individual components (and may be answering the questions in unexpected ways!)
Making the questions harder will often make things worse, on its own, because the student will get stuck and demotivated and hard-questions-for-the-sake-of-being-hard will seem pointless to them.
I do use this as a strategy but only when I'm confident that the student has a very good understanding of what's going on.
If they're not writing down the steps, it's more often that they are demonstrating that they don't have a good enough level of understanding to do this. (This also applies to "gifted and talented" students)