Then why make the checksum bits part of the stride in the first place? It doesn't need to be guessable because this part can be derived after the private key is known, so passing the checksum bits makes no sense in this context because it lets the program look for invalid checksums as if it were part of the private key.
Because checksum has impact on addition result.
Example (in dec):
Imagine you have stride 530. And you have checksum 70.
If I do like you said, so I will remove 2 last digits of stride, I will have private keys:
5, 10, 15, 20, 25.
But if I do the correct addition and then remove 2 last digits, I will have:
600->6, 1130->11, 1650->16, 2180->21, 2710->27.
And the problem is that different some group of checksums will create the same private keys and some checksums completely different.