You are effectively increasing collision risk by an arbitrary amount by running hash output as input to a crc algorithm.

Kids, don't roll your own security.

This is if you compare two hashes and they look really similar but you want to be really sure.

Of course a real equality check is better but visual check of original hash + this is better than visual check alone.

After: four hashes that don't pass a manual check

The short ones are there so you can easily spot the collision in the long one, even if the start and the end are the same. If you read just the short ones your criticism applies, but that was not the idea. You read the long one first, then the short one. This is a logical AND not a logical OR, thus it gets harder to make both collide at once (because there are less similar looking values for the first one that produce the same values in the second one + your attacker might not know which one you are using).

Maybe if you read my comment, you will also realize I pointed out that CRC8 is the wrong choice for this, but I was on my phone and this was the hash calculator I found first.