Alright. Here it comes.
Antarctic Summer.
At the region directly around the southernmost part of the Earth, which here I will refer to as the South Pole (despite your claims that there is no such thing.) In the area directly around the south pole, you know, the area at the very edge of your Earth? Well, it experiences 24-hour sun around the summer solstice. Therefore, on your model, the sun would have to illuminate the entire Earth at once. This would mean that nowhere on Earth would it be night! Explain that!
The Sun using a "spotlight" affect is invoked:

This is what is supposed to happen with the Sun acting like a "spotlight". When FEers say "spotlight", a nice normal cone-shaped spotlight is visualized by people (this is a FE deception that sounds somewhat reasonable initially). This only happens on a
couple days of the FE year (~June, hence the deception). The rest of the year the spotlight is weird. No explanation is ever given for why such odd shapes (a "perfect" straight line during the equinox, or an "anti-spotlight" during the Antarctic Summer) happen.
Furthermore, because of problems or the lack of Astronomy 101 knowledge, what is never discussed is that virtually EVERYTHING in the FE sky/heavens must exhibit a "spotlight" affect (the "spotlight" having different shapes depending on latitude
at the same time). The Moon, planets, some stars, nebulas and galaxies, travel in the same area of the sky as the Sun - the ecliptic. So this "spotlight" needs to affect EVERYTHING in the sky somehow. It must be an atmospheric (atmoplanic?) phenomenon.
This also implies, contrary to some people's knowledge of how the FE concept needs to fit together, that the Sun does NOT illuminate the Moon - the Moon is self-illuminating. Now how it does that becomes another question. This leads to bizarre explanations like Moonshramps. This is an example of one explanation "fitting" one situation ("spotlight") causing more problems down the line (self-illuminating Moon) with more bizarre explanations (Moonshramps) as each level has to account for the effects of the previous level(s).