It is possible, it has worked, and will work.
It is just a matter of time.
However, people are glossing over the nigh-energy-neutron part.
Those neutrons are indeed absorbed by the blanket material. If you have enough of it. And some is going to escape, and those neutrons will cause damage to living tissue too.
What they are doing is just minimizing it.
That blanket material becomes radioactive after that happens. It is called "activated".
Good luck with that.