Does nothing in what way?
QAbstractItemModel doesn't contain any data, it is an abstract interface that you can implement any way you like. When you create your implementation of the that interface you control how it behaves. If you want a view to allow checking of an item from your model then you need to return Qt::ItemIsUserCheckable amongst the flags() for the item (which should be editable). You will also need to do something sane with Qt::CheckStateRole in the implementation of data() and setData().
If you want a function like QStandardItem::setCheckable() to apply check-ability on an item-by-item basis then you need to add the method to your implementation and find somewhere to store the check-ability flags against an item in your model implementation. One solution is to use another role on the item to store/retrieve the check-ability attribute (i.e. like QStandardItemModel does) but you could equally use another structure. How you do it is entirely up to you because only you know what the data being presented through the model looks like.
Whether a view does anything with the checkable state is another question.
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