Where exactly is this cache residing? Not in the cable. So if it exists at all, it would be beyond the input receiver and would have nothing to do with the cable.
It has everything to do with the cable. As long as the signal gets to the receiver where the cache resides with the bits "distinguishable," even if highly attenuated, the signal is regenerated. In other words, you don't need to spend 100s of dollars to get the signal to a receiving end when a $11 to 20$ cable will give the same exact result as long as it is in line with standard specifications. You don't have to spend a lot of money to buy an in-spec cable.
If shielding is poor (or the cable is too long) and the signal has degraded enough that the input receiver is unable to recognize it, you are hosed.
And why do you think this is contrary to any of the points I am making? Read what I wrote...
There are plenty of cheap cables that are built to proper specifications. Spending 100s and 1000s won't get you any more in-spec than the standard demands.
I have no clue whether or not HDMI supports any error detection or correction. Interference can be transient so that drop outs are the result. If it happened frequently you might notice it.
Whatever the case may be, you still don't have to spend excessive amounts of money to get a well built, in-spec cable. People that think so are either delusional or trying to sell you something...