I understand the frustration this causes you, along with anger.
It is normal to feel this way, and certainly justifiable.
Visitation should not be with held because of non payment.
The decision to do so can be misinterpreted by your children now and down the road.
I would say respectful boundaries should never be compromised. Your child has the right to see the father.
With the description you have given, your EX will seal his own fate all by himself. He won't need you to block visits, he will stop all by himself.
It appears from what you describe, your EX wants to exercise
His rights for visitation, probably to "look good to others, or feel better" about himself. It is about him.
What will happen is YOU will remain the solid parent the children can count on and trust.
When your children are older, they will form their own
Trust me, set respectful boundaries for visits always emphazing the focus of children....won't be many visits.
There will be excuses.
Lived through this years ago myself.
My adult son respects me, has no contact with his father.