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What if Alonzo didn't have that disease? How many players have done better than him in their first 8 years in the league?

Alonzo was a beast. #1 high school recruit of his class, Great player at Georgetown, was drafted 2nd behind shaq. He doesn't have a lot of accolades (2x all-def, 2x all-nba, 7x all-star, 2x DPOY, 1 ring as an old bench player, 2X block champion) because the league was filled with great bigs and he didn't really have that starpower.
Anyway, the 2 years before they found out about his disease, he ranked 2nd and 3rd for mvp. He also has 2 DPOYs.
Alonzo was a 6-9 warrior, built like a truck, with a crazy 7'6.5" wingspan.
Obviously, he was a monster defender (certainly one of the 20 best of all times). He was an incredible rim protector (averaged 2.8 blocks for his career), a great post defender, and he was a little bit more switchable than the standard center of the 90s. He was a tough guy. But he was also a very good offensive player (but not stellar) I would compare him to a better bam adebayo. Both play for the heat, both are not overly tall, but very physical, muscular, long arms centers, whose claim to fame is defense but they also have a good offensive game. Alonzo had a nice face up game, he had a decent jumper and he could take it to the rack ferociously. He had some post moves. He also had an amazing free throw rate.

In his first 8 years, he never averaged less than 19.2 points. His averages were 21.1/10.1/1.5 assists/0.6 steals/3.1 blocks (lol) on a very high 58,7 TS%. The league average for that stretch of years was about 53%, so he was almost +6RTS%. Admittely, even if 21 on +6RTS% is pretty amazing, he was a very good, but not stellar offensive player. He wasn't the type of offensive player that would pose a tachtical problem to opposing teams, like, he was a good scorer but he wasn't like shaq where defenses would have to collapse, or dirk who would stretch the floor etc, he also wasn't a very good passer, but yeah, he was a guy who knew how to give you a consistent, VERY efficient 20-25.
So, with Alonzo, we have a guy who, starting from his rookie season, played DPOY defense while giving you 21.1/10.1 on +6%RTS, in a low pace and scoring era. And he did it in winning teams. He made the playoffs in 7 of those 8 years, made the ECF once and won a couple other playoff series.
Other than that, he was at his best just when the disease came out. In those 2 seasons, he won his 2 dpoys, and got his only 2 defensive and all-nba selections. Like I said, he also got a 2nd place and then 3rd in place in mvp. Truth be told, in those 2 years, he was as good as anybody not named shaq.
Obviously, after his disease, his effective career ended, and he was lucky enough to be cleared and stick in the league until 37 and win a ring in 06. He's the 3rd best player in miami heat history after Wade and Lebron.

Now. What if he didn't have the disease? What would have happened, how high would he be ranked? And, how many players have done better than him in their first 8 years in the league?

Alonzo Mourning was a great player who is rarely mentioned but Shaq and the other alltime greats of his era remember him. In 99 and 2000 he had just reached his peak and looked like he was going to be a legit star big, moreso than he already was, for another few years. He wasn't Shaq but I think he may have been almost as good in 2006 and 07 and with Wade and the rest of that Heat squad they could've still won that championship. He was, as you said, a very good but not great scorer, he had a number of offensive skills and a nice jump shot. He was an absolute beast defensively, one of the best ever. Others like Russell, Chamberlain, Olajuwon, Robinson, even Mutombo, are mentioned among alltime great defensive bigs, but Mourning is right there with them.

I rate him higher than Dwight for peak and prime. His effectiveness for his teams were at the same level as Barkley, Giannis, AD and some other popular bigs. The Hornets went from awful to playoffs the following season because of Mourning. The Heat became a top 4 team with him and Tim Hardaway, with Mourning being slightly better and their anchor.

Definitely unfair that he got that disease and his career was severely effected.

I know that isn't what the OP asked, but if Alonzo stays healthy and doesn't have to sit out the entire 2002-03 season, the Heat are way better that season and probably have no chance of drafting Wade.