The power divider is using LC networks and achieves impedance matching only for a small frequency range (if designed correctly), e.g. 28 MHz as claimed in the picture filename. It can never work over 1:10 frequency range.
FVM is right that the circuit in your pic will never do wideband, but I have seen similar using binocular (2-hole) ferrites and bifilar wire. I'm uncertain those will handle 1Watt.
We should quickly clarify the terms. In the post #3 design, "ferrite based" actually means lumped LC, specifically based on single pi-filter. As said it can't be wideband.
A transformer based 10 - 100 MHz power divider would be well possible using ferrites, using the basic circuit linked in post #4. Another approach would be a multi-section lumped LC circuit, the lumped equivalent of a multi section transmission line Johnson power divider. It could possibly use ferrite core inductors.
Okay, I was being premature. When building a power divider, I was thinking of using some kind of transformer with 2 secondary windings. Most ferrites have a limited bandwidth. When looking at the amidon datasheets for example, I would look at ferrite type materials. Material 43 runs from 1-50 MHz and material 61 goes from 10-200.