If the Earth's atmosphere is rotating at the same speed as Earth, then the atmosphere must be rotating much faster at the equator than at the poles. If you spin a ball covered in oil, it will form rings. Also Jupiter has rings. So why doesn't the Earth have rings of weather too?
[Physics] Why doesn’t Earth’s atmosphere form bands due to different rotational speeds
atmospheric scienceearthweather
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Using data from here, increasing Venus' rotational speed to match Earth's would require about $\:\mathrm{1.5\times 10^{29}\ J}$.
It's insolation is about $\:\mathrm{3\times 10^{17}\ W}$, so assuming that somehow all this energy could be transferred to rotation, it would take about 16000 years - not absurdly long actually.
There are a couple of ways the atmosphere can be viewed as being "thicker" at the equator than at the poles. One sense is the mass per unit area of all of the air overhead, from sea level to outer space, at the equator vs at the North Pole. Atmospheric pressure at sea level, being essentially a potential, is on average pretty much constant worldwide when averaged out over the course of years.
Since atmospheric pressure is the weight per unit area of all of the air overhead, those places where acceleration due to gravity is low must necessarily support more air in terms of mass to achieve the same pressure than areas where gravitational acceleration is high. Gravitational acceleration at sea level is a bit less at the equator than at the poles, making the atmosphere at the equator a tiny bit "thicker" than the atmosphere over the North Pole, by about half a percent.
This is a tiny effect. It is not what people mean when they say the atmosphere is thicker at the equator. The tropopause is considerably higher over equatorial regions (more specifically, over the intertropical convergence zone, or ITCZ) than it is over polar regions. The tropopause can 20 km above sea level or higher at the ITCZ and only 4 km above sea level at the poles. The boundary between the troposphere and stratosphere is essentially non-existent at the South Pole during parts of the winter.
The small decrease in gravitation (including centrifugal acceleration) from the poles to the equator accounts for only a tiny bit of that large change in troposphere height. In fact, Of the five reasons listed in the question, none is primary. The key reason for the tropopause height reaching a maximum at the ITCZ is the general circulation of the atmosphere, with the ITCZ itself playing a key role.
The ITCZ is where the moisture-laden northern and southern hemisphere trade winds meet at the surface, are driven to great heights due to convection and latent heat, and finally separate to flow northward and southward near the top of the troposphere. It is the strong convection and associated very strong thunderstorms created by this meeting of these atmospheres that pushes the tropopause to great heights at the ITCZ. Tropical cyclones and CAPE-driven thunderstorms elsewhere can also push the troposphere to great heights, but these are transient local effects compared to globe-spanning ITCZ.
The polar regions generally have very little, if any convection. Oftentimes they suffer descending rather than rising air, pulling the tropopause downward. The tropopause is also pulled downward at the jet streams, particularly the polar jet.
Best Answer
The short answer is -- there are bands! They behave very similar to the bands on Jupiter, but are not as pronounced. And we don't have a really unappealing colored atmosphere to show us what the bands look like.
Here is an example of what they look like (source):
There are two bands along each side of the equator. Another set of bands starts 30 degrees north and south of the equator. And another band starts 30 degrees further north and south (at 60 degrees total).
You'll also note that these differences in wind in the same direction of rotation also causes wind to form in the north-south direction. All of this is what drives the major weather systems.
Consider the US. Weather systems will typically move from west to east. Atlantic hurricanes form in the tropical band off the coast of Africa. They form here because the wind is relatively calm and there is little north/south shearing. They then move westward in the tropical band while also moving north due to the Coriolis forces. As they move north, they begin to encounter the westerly winds that are characteristic of the mid-latitude cell. This will eventually turn them around so they move north-east along the US coastline until turning due-east and moving towards Europe (which in turn induces a southward drift due to Coriolis forces).
Here are what several of these hurricane paths look like (source):
These bands are not typically readily apparent. Mostly this is because our atmosphere is transparent so we have no way to "visualize" the bands. It is possible to sometimes capture bands however. A band of rainfall in the intertropical convergence zone around the equator is captured in this GOES satellite image (source):
Also, these bands are climatological features and not meteorological features. This means their structure is not always apparent instantaneously but appear in a time-averaged view of the atmosphere. It turns out that NOAA released a time-lapsed video of 10 years worth of GOES-12 images and the bands become pretty apparent!
@DavidHammen found another great video looking at the infrared signature caused by water vapor in the air by the GOES-13 satellite shows the bands better than looking at the visible cloud cover.