I think people are conflating two separate things here:
The EFL fit and proper test is where they filter out the likes of William Storey. Everyone who has voting shares in a football club has to pass this test. It's very easy to pass, just don't be a fraudster like William.
The other EFL part is that they have to approve the deal itself. This is where - for a completely random example - they might question the business plan of two people who wish to send vast quantities of the club's future income to a former owner. In this sense, it definitely matters if the majority shareholder would be person X or person Y, and that changed during the process, because that's a substantial change in the funding plan and who would ultimately be answerable if they fuck it up.
In essence: Good people sometimes do bad things, or at least things that the EFL would not wish to happen, so they vet the individuals, but they also vet their plans for ownership and can stop a deal going through if they have concerns. This is what they tried to do with Donald - he passed the fit and proper person test, but they had major concerns about how he proposed to fund his ownership.