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I thought this was going to be about an implementation of transformer models in pure R and I wondered... why?
I thought it was going to be about implementing transformer models in a way that fits well with some special kind of hardware like those green arrays or whatever they are called (the low energy use, highly parallel (but maybe low clock speed?) ones)
Meanwhile, I was so happy to finally see an article about transformers that is really about transformers and not some programming thing.
Grandpa's transformers don't come with huggingface emojis
I have yet to get a straight answer on what the actual benefits/trade offs are with R, C, and EI cored transformers as well as torroids. My only exposure to these are as output transformers on tube amplifiers. There is plenty of debate on forums but would love to hear from an engineer about what type works best in which situations.
Power loss, EM interference, and probably some impedance and frequency response characteristics too (not sure about the last two)
In addition to the lower flux leakage as mentioned in this article, there is a benefit of R-core and toroidal transformers which is reduction in the strains due to magnetorestriction that happens, which is what can make transformers- especially cheaply made EI-core transformers- have "hum" at 2x the AC fundamental frequency (e.g. 100 or 120hz for mains powered devices).
Given your name, the practical answer is that there is no difference assuming they are properly selected and implemented in the circuit. The exception being the EI core and SE outputs, EI cores were the only ones made with airgaps last I was paying attention. Audio is just not as picky as some would like to make it out to be, sure a torroid in the power supply will let us get away with a more compact layout and make it easier to get the noise specs we want but it is not that difficult to do with an EI core. When you get down to it, they are each different in some vague but highly marketable way.

Edit: I am over simplifying things, there are differences but my point is that in audio work the design execution is what matters.

Clever and interesting! But not new. FWIW, I remember repairing a PA or musical instrument amplifier in the 1990's whose power transformer featured this type of core and bobbins. Its novel appearance and intriguing construction attracted my attention immediately! :)
Is this to reduce reactance?
Reactance is the only thing really limiting current flow in the primary...without it (which can be simulated by shorting the secondary) only the resistance of the wire would limit current flow. The subsequent joule heating of the transformer would result in thermal runaway without it.

The main advantage of this setup is to drastically reduce interwinding capacitance and DC leakage current.