Would AJ becoming a 3x HW champ be more impressive than one continuous reign?

Definately: YES!!!

Why?

Because especially in combat sport you see many fighters who are mentally destroyed after defeats, prime example is Prince Naseem Hamed.

AJ was mentally shattered after his 2nd loss to Usyk, he cried during the post-fight press conference. I guess 80% of the boxing people thought he was done.

The way how he looks today mentally is just incredible. He bounced back, he never stopped.

If he becomes a 3 times world champion, that would be an outstanding feat.

I would compare it to 2001 Wimbledon champion Goran Ivanisevic in tennis (i am sure @Goran_ remembers that ). He was runner up 3 times before, in 1992 he lost to Andre Agassi, in 1994 and 1998 to Pete Sampras. He lost in 5 sets to Agassi and Sampras in 1998, and he cried after that last loss.

In 2001 he came back to Wimbledon with a wild card...and became the first and only Wimbledon champion in history doing so, winning the title with a wild card. He didnt defeat Agassi or Sampras to win the title, but Agassi lost to australian Pat Rafter, who was already a 2 time US Open champion.
Ivanisevic defeated Rafter in a 5 set thriller, and his last service game was unforgetable, many aces and double faults, his nerves took over, but he did it.

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If AJ becomes a 3 times champ, it would just be a great thing. Someone comes back is always very impressive.

 

Only Ali was LINEAL HW Champion 3 times. Lewis (2), Holyfield (2), and for Vitali I'm not sure if he was ever a lineal HW champion.
Ironically, Anthony Joshua I'm sure was never a lineal HW Champion.
In the modern understanding of boxing, it is too much to ask a boxer to be a 3-time lineal champion.

P.S. I know that lineal championship is not the topic, and that I went off topic