You are right Woltz and Turnbull

Extracts:
Originally Posted by The Last Woltz
By this point, Michael's only concern was legal liability, not appearing legitimate.
My misunderstanding of Woltz's post

The priority at the time of senate hearing was legal liability not appearing legitimate - did not mean given up trying to “appearing legitimate”
Originally Posted by Turnbull
Michael never gave up on trying to appear "legitimate." He was obsessed with it. Look at all the money he gave to the Church so he could be invested as a Knight of St. Sebastian, his party, and the press corps he invited to witness it--all while serving, as Vincent put it, as "the Pope" of the Commission.

Originally Posted by Turnbull
Michael fooling himself about "legitimacy" was his undoing throughout the Trilogy. A serious essay could be written about how frustrated Michael was about "legitimacy" and his failure to achieve it

What could have made Godfather 3 better?
Originally Posted by johnny ola
I got the impression that Michael finally got the point of being considered legitimate

Whilst Michael was serving as "the Pope" of the Commission, Michael seemed to have managed to achieve at least his 'pretend'! "legitimacy" to some degree

The above not dissimilar to “legitimacy” in Nevada but Pentangeli's crime operation in New York was still called Corleone

The Godfather Wiki - Immobiliare
Michael Corleone bought a large block of [Immobiliare] stock during the 1970s, eventually becoming the company's largest single shareholder in 1979
[separate to trying to buy the Vatican's stake for controlling interest]