You're expecting too much from a $120 saw and $35 thin kerf blade. Power tools in this price range just aren't manufactured to ultra-tight tolerances because there is a point of diminishing returns for the manufacturer, and they start cutting corners in some places in order to hit a certain price point.
You can try cleaning your arbor or replacing the washers on either side of the blade with higher-quality ones. You may be able to tell if the washers are not flat, or if one or both is inconsistent in thickness from one side to the other.
If you're getting 4-5 thousandths of an inch runout (slightly more than the diameter of a human hair) along some parts of your blade, that means mating 2 cut pieces may give you a gap as wide as 1/100 inch. Most people wouldn't pay attention to a gap this size when looking at installed crown molding from 4+ feet away, but even so, carpentry projects inherently have some amount of slop because time is money, and a skilled carpenter will have plenty of techniques for working around and hiding imperfections where it matters.
On top of that, whatever you measure with the blade in a static state most likely will differ when the blade is spinning at 5000 RPM, especially with a thin kerf blade whose plate will be less resistant to flexing than a full-kerf blade. Based on your experimentation, it seems this is not the major factor since the original blade produces the same results.
Considering the workarounds, you don't need to buy a $400 shooting plane; you can just as well use a $30 hand plane and shooting board, or clean up the edges with your crosscut sled.
That said, there is no reason to throw out your miter saw. At some point you may want to crosscut a very long board, which will be awkward on a table saw and may require you to move your table saw or rearrange your shop to accommodate the operation.