I find some of this to be true. Vince typically did not give sustained pushes to guys who became big stars before WWE. Initially Vince stocked his roster with stars established elsewhere, some major (Steamboat, Piper, Valentine, Jake Roberts) some less so (Savage) but they had almost no change in character or presentation. Around 1986-87 Vince started creating distinctly unique gimmicks for recently signed top stars, much different from their prior success ala Million Dollar Man, Mr Perfect, The Red Rooster (there are stories that Terry Taylor turned down the Mr Perfect gimmick, great career choice). Still, there were individual circumstances where top stars joined WWE and were not subject to major changes to their name or presentation. Kerry Von Erich, Tully Blanchard & Arn Anderson, and LOD were among those. Ravishing Rick Rude was a new nickname but essentially the same character and presentation he played in the NWA. Despite not being "homegrown" or playing a completely different character they all got significant pushes. Von Erich and Blanchard were derailed by drug issues, Anderson went back to WCW for a reduced schedule and to be with former partner Ric Flair, LOD remained in WWE for a decade, into the Monday Night Wars and The Attitude Era. Hawk's untimely death of a heart attack ended the team but Animal remained in WWE well into the last decade. Most famously Shawn Michaels was a major star in the AWA, played the same character for years in WWE, then when his tag team The Rockers was becoming stale Michaels recieved a major push as a singles star, embarking on a HOF career. Ric Flair was clearly established as the face of the NWA in the 80s and was a major player in The Monday Night Wars for WCW. In between he defeated the entire WWE Roster to win the World Title at Royal Rumble and dominated the programming for most of an 18 month run, then was an integral part along with Michaels of several major angles in the last decade, including the pushes of Randy Orton and Batista, WrestleMania bout vs Undertaker, and the biggest retirement angle in wrestling history. Both were treated quite well despite not initially being "WWE creations" or undergoing drastic changes to their name and presentation.
If Sting would have come in when Warrior did he may have gotten lost in the shuffle. Warrior had a "Goldberg esque" monster push and persona. It was organic with the audience in a way that many angles are not. No doubt as a complete character and performer Sting was way better. Warrior had a brief run, Sting is a legend. Sting needed work however to become that good, an opportunity he may not have gotten in WWE, especially coming in at the same time as Warrior and Von Erich.
If he had stayed in the NWA and became a star, his best chance to jump was 1993-94. WWE was struggling, constantly looking for a major star in the post Hogan era. Guys like Kevin Nash & HBK as well as former NWA guy Lex Luger all benefited. Sting would have had a good chance to become one of the top stars in the company.
You're missing the point to an extent, most of the guys you mention did NOT get the big push, to the main event for a sustained period of time however they were presented.
Some got secondary titles, for a relatively short period of time (Rude got the IC for 3 months, Perfect for less than a year both reigns) but they did not move up the card afterwards in the Bret Hart style push that is now so commonplace from IC to World within 2-3 years.
Perfect, Rude, Steamboat, Von Erich, Bossman did not wrestle main events often, at maximum one PPV or feud. Part of it was down to their size or lack of long term marketability in Vince's eyes, but the other part was that they were not "Vince creations", they all had some kind of success elsewhere that meant they were known before the WWF. If Kerry had gotten the push, they would have had to bring in the whole clan, acknowledge or completely ignore the NWA World title etc, same for Perfect and the AWA the latter would have been jarring ("Perfect has his first World title at last"... erm no it's his 2nd... In Hennig's case when he made his big return in 92, when you thought push and a World title feud with Bret was on the cards... it wasn't and it was Luger and the IC title that he again pursued...
Most outsiders got some push but never for long and always hitting a ceiling, Flair was really the first one to break that ceiling and let Luger and Nash in although it's arguable whether Nash had any actual name value in WCW, Diesel was certainly a Vince creation as was "Stars and Stripes" Lex... the one who had been a Horseman had been all but wiped out by then.
The Shawn Michaels who got the World title and became a HOF er was not "Rocker" Shawn from the AWA. Vince created "HBK" as a gimmick for that early run (that Shane Douglas turned down no less) and that did for his early run but it was the DX Shawn, something far removed and 10 years on from his AWA persona that got him his first World title. The Rockers never got serious push and the LOD were not treated as the dominant team but often behind WWE own teams like the Natural Disasters and Money Inc.
DiBiase and Piper were slightly different, as they had been around the WWWF pre Wrestlemania era or were integral to the birth of it but even Piper never got many World title matches and DiBiase, past the Megabucks never got another main event push ... They were always presented as "one tier down" from Hogan, Warrior, Savage etc which was higher than any of the other guys. The DiBiase win or near loss became an important part of any singles push in that era. Bret's near miss against DiBiase at Survivor Series 90 was the moment VKM could see he would work as a singles star.
Sting's ideal window was 1991, when Flair came over, had Vince signed Sting instead of Flair then I think it would have worked. Had Sting come over to help Hogan and Savage challenge Jake Roberts, Taker and Sid as "someone who knows them all well" and winning that Rumble instead of Flair. Warrior's return would not have been needed and Flair's debut could have come at WM8, attacking Sting and challenging him for the title after beating Undertaker (MegaPowers v Sid and Jake would have been the other main event)