INRE: "decrease as we move away from the equator on either side towards the poles" Play the animation "Land Surface Temperature" on https://earthobservatory.nasa.gov/global-maps/MOD_LSTD_M , there are similar ones for air temperatures at various altitudes, and ocean surface. See attached graphic "Air flow on a planet with no rotation and no water".
For any given spot on Earth, the amount of change (variation) in temperature and the max / min at a given point in time is dominated by those factors, not the distance from the equator, the 'equator' is a convenient artificial construct for coordinate systems. A more useful construct are the Global Atmospheric Circulations ( https://www.noaa.gov/jetstream/global/global-atmospheric-circulations ), somewhat roughly approximated by the Tropic of cancer and Tropic of Capricorn, and Arctic and Antarctic circles) ). Some locales are even more dominated by factors such as altitude ( the Tibetan Plateau is called the 'Third Pole").
Yes, due to the spherical shape of the Earth, sunlight falls on different parts at different angles. Direct and focused sun rays falls on the equator and hence, the regions here are hotter and warmer. The Polar Regions receive diffused sun rays, which is why the areas there are colder.When the sun's rays strike Earth's surface near the equator, the incoming solar radiation is more direct (nearly perpendicular or closer to a 90˚ angle). Therefore, the solar radiation is concentrated over a smaller surface area, causing warmer temperatures. Because the Earth is nearly round, the equator receives direct light, and the poles receive slanted light, with a gradation in between. Due to the differential heating of the Earth's surface it is always warmer at the equator than at the poles. The Equator, at 0° latitude, receives a maximum intensity of the sun's rays all year. Because the Earth is round, the frigid Polar Regions never get a high sun, and because of the tilted axis of rotation, these areas receive no sun at all during part of the year. Average annual temperatures in equatorial lowlands are around 31 °C (88 °F) during the afternoon and 23 °C (73 °F) around sunrise. Rainfall is very high away from cold ocean current upwelling zones, from 2,500 to 3,500 mm (100 to 140 in) per year. Latitude is a circle horizontal to its orbital plane. In any sphere the circumference is lengthier at 0°. So equator is lengthiest latitude and the degree increases or move away from equator to pole the circumference of globe decreases hence latitudinal length also decreases. The length of latitude slowly decreases towards the poles due to the rotation of the earth because as the earth rotates a centrifugal force is generated which causes change in its shape that makes it oblate spheroid. As you move away from the equator towards the poles, the earth's surface becomes more angled to the incoming sunlight due to the spherical shape of the earth. Because of this, the intensity of sunlight received decreases as we move from the equator to poles. Hence, temperature decreases as latitude increases.
Without addressing the other factual errors ( i.e. the influence and mechanism of the Coriolis Effect), the incident solar radiation is not the dominant factor for any given location on Earth. If we consider ecological zones which a heavily dependent on energy available for photosynthesis from 'direct' sunlight, of note are the North American forest's species which extend from Tropic of Cancer ( which is the 'solar' equator in the summer ) at the tip of Mexico's Baja peninsula to the Brookes Range in Alaska above the Arctic Circle - or just consider any East to West latitude line in Norway.
If what you claim holds true, why aren't other climate zones symmetric across the equator, or even more dramatically the differences between the North and South Polar regions? ( see "Polar Opposites: the Arctic and Antarctic" at https://www.climate.gov/news-features/understanding-climate/polar-opposites-arctic-and-antarctic ). To large extent, the only reason the Earth supports life over most of it's surface is because all these other factors dominate over the pure geometry of the incident radiation flux.