Voter Id laws won’t make any difference to absentee ballot or early ballot fraud. Some other strategy needs to be found for that.
Though your point is accurate, the impact of such laws may affect other types of fraud.
Simple solution:
1. Vote in person, with id, at the time designated, or provide hard evidence of your reason for voting early at a designated and monitored location; election day rosters to clearly show that the vote had already been cast.
2. Total exception for military, military families, overseas workers / US representatives overseas, and employees deployed within CONUS; vote only by absentee ballot provided (timely) by the employer and accounted for by that employer. (Easy to do, just reassign a pot load of "Equal Opportunity/diversity employees to a job that would actually benefit society.)
3. Heavy fines for any employer not in compliance and hard time for any voter caught in a scam.
4. Only hard copy ballots accounted for by US Marshals; no electronic gimmicks because there will always be new ways of hacking or rigging the equipment.
Seriously: If someone is too lazy, too incompetent, or otherwise not going to take time to cast a ballot - I don't want them voting by any means.