There are lawyers much smarter than me involved in this process, and I can almost guarantee that it was NECESSARY to invoke executive privilege in this case.
When a governing body with the authority to issue a subpoena does so, the recipient is obligated to either answer the subpoena or assert a legal reason -- usually a privilege enshrined in the law -- not to do so. A typical response in a legal proceeding would have been to assert that the requested information was covered under lawyer-client privilege (for example).
So the DOJ could have:
1. Provided the information to Congress.
2. Ignored the subpoena.
3. Refused to provide the information, while giving a reason that had no basis in law.
4. Asserted a legal privilege in refusing to turn over the information.
I'm not sure exactly what your point is here. Option 1 was off the table because it would be illegal. So which of the three remaining options would NOT have "looked like the coverup the Dems have been claiming all along?"
Your reason #3 is applicable in this case: that the law prohibits any further release.
That is so glaringly true that even the diehard Leftist press could not refute it.