Agreed. The states should change the rules. But in this specific circumstance (for what the opinion is based on), they didn't. The courts changed it after a challenge. Kavanaugh seems to be vesting the rights to change election laws with the state legislature, and not the courts. I think that is pretty much in line with what I would expect from him and other conservatives, this pandemic and unique circumstances you reference above be damned. Problem is obviously where the state legislature is controlled by republicans = no changes.
I think the part to focus on in Kavanaugh's concurrence is 'or as soon as possible thereafter.' That could mean a day, 3 days, a week, etc. based on each state's rules. Note, there aren't challenges to laws where state legislatures have different rules (for instance, Texas allows for the receipt of mail in ballots up to 24 hours after the election date). He referenced a few other states doing the same or having deadlines even further out. The key there is that the legislature enacted those rules, not the courts after a challenge.
I think the problem here is more-so with the state legislature(s) than the opinion itself.