How to remove legend items with PyQGIS without removing the layer?

This is code adapted for QGIS 3 from this answer. It adds all layers except one specified. You could swap this out for a list, or conversely, use the layers you want to keep in rather than those you want to leave out.

l = QgsProject.instance().layoutManager()
    
for layout in l.printLayouts():    
    legend = QgsLayoutItemLegend(layout)
    root = QgsLayerTree()
    for lyr in iface.mapCanvas().layers():
        if lyr.name() != 'Unwanted layer':  
            root.addLayer(lyr)
        legend.model().setRootGroup(root)
        layout.addItem(legend)

In place of if lyr.name() != 'Unwanted layer': you could use

if lyr.name() not in [list, of, unwanted, layer, names]: or

if lyr.name() in [list, of, wanted, layer, names]:

Matt Needle, your solution started to work after I've forced qt to process the bufferd events, before iterating through layers. Thank you for your hint.

from PyQt5 import QtWidgets
inst = QtWidgets.QApplication.instance()
qapp = QtWidgets.qApp
qapp.processEvents()

l = QgsProject.instance().layoutManager()

for layout in l.printLayouts():    
    legend = QgsLayoutItemLegend(layout)
    root = QgsLayerTree()
    for lyr in iface.mapCanvas().layers():
        if lyr.name() != 'Unwanted layer':  
            root.addLayer(lyr)
        legend.model().setRootGroup(root)
        layout.addItem(legend)