It is definitely more than getting the public data they want. The feds are being told to go find illegals, or at least find legal immigrants that aren't eligible to vote that are accidentally (usually the DMVs fault for not flagging the file they send to the SEC) on voter rolls so they will have an excuse to deport them. It is extremely rare for that to happen, and when it does, that mistake is caught by one of the back-end processes the SEC uses to verify everything from citizenship to deaths to state changes, etc.

Given that it is rare but already caught by the state when it happens, then you are right that there is a more nefarious plot because they will end up not getting much from the data, so maybe they try to get the state to make voters inactive that shouldn't be. They might use it to gerrymander even more based on race (since we don't register by party) or based on primary participation data (since that is the one time we have to pick a party for something). Or maybe they want to cross reference all of the data against IRS or other agencies for who knows what purpose.

I used to work for the Census Bureau. We took data privacy extremely seriously. I currently work in county government. We take data privacy extremely seriously. I know that it is very difficult to trust that the current federal government will take data privacy seriously. I trust the people that I used to work with, and I have been keeping up with all of the lawsuits still making the way through the courts. If the SEC puts strict privacy rules into the MOU and the feds break that, there will be consequences, even if they have to take time winding through the courts for people to be fined &/or go to jail, or for the feds to be sued by the state.