Some people think disenfranchisement is bad. Others see it as useful.
Specifically, PartyB thinks those people with inadequate ID skew toward PartyA voters. This has been the accepted wisdom for decades. So they are incentivized to make it harder for them to vote.
Interestingly though, PartyB might be wrong about the current population. PartyA, and those against disenfranchisement and imaginary crises in general (I count myself in this third group), do not want to blow up centuries of precedent especially if the consequences are likely to be undemocratic and unfair.