QLineEdit ignores visibility change in added QAction

I created a QLineEdit and adding a QAction.
When switching the QAction to invisible, it stays visible in the QLineEdit. It does not respond to clicks, but is still there. It should become invisible.

Example code:

QLineEdit *edit = new QLineEdit(this);
QAction *action = edit->addAction(QIcon("/path/to/icon"), QLineEdit::ActionPosition::LeadingPosition);
action->setVisible(false);