This is kind of a case-by-case basis for each character and game
Smash 64: Most of the characters were obvious choices for a Nintendo video game at the time. Since all the franchises were featured in the SNES era for the sole exception of Pokemon which was just a HUGE success on the Game boy and media in general at the time. The only character that might arguably reach "demand" levels in Smash 64 was funnily enough Jigglypuff for being one of the most popular pokemon in Japan at the time. Albeit it also helped that Jigglypuff could be cloned off Kirby.
Melee: Many of the newcomers in Melee are characters that were considered for Smash 64 or naturally considered the next steps for inclusion for already represented series. Though Melee was also the first instance of clones being added even if obviously they were never asked for and even cutting corners for an incredibly requested character
into a heavier, slower version of another character
Brawl: Brawl in turn also had characters that were considered for Melee. Meta Knight and Dedede were left out of Melee mostly for concerns of Sakurai overrepping his own series. But when they both got some high demand for Brawl he put them in at last. Wario, Diddy Kong, and Olimar all probably had followings after Melee as well.
But of course there's still the 3rd party characters to consider when covering what Brawl did for fans. Snake was mainly a Kojima request. But Sonic on the other hand? In the times before 3rd party characters were considered not very probable. Sonic was probably the one most brought up should the "impossible" happen. "Wouldn't it be cool to have Mario fight Sonic in Smash?" I'm very willing to bet was something brought up if there were any discussions about 3rd parties before we knew it would ever happen. Then there was that EGM April fools joke of Sonic and Tails in Melee, and then Snake's surprise announcement for Brawl took the internet by storm. And that quickly rose up the people who thought it would be cool for Sonic to get in to Smash and turn it into "This can actually happen!". Sakurai even did have Sonic in Brawl's project plan that was initially denied by Sega but they changed their mind just fast enough for Nintendo and Sakurai to simply delay the game a little more to find time to squeeze Sonic in. If Brawl had been made more recently though, Sonic probably would of been Brawl's first DLC character much like Mewtwo was in Smash 4. Fans absolutely still had an impact to bring Sonic in the game. Cause if Nintendo and/or Sakurai felt the game was too far in development and that the fans could handle no Sonic despite being by far the most requested 3rd party at the time. They could have denied Sega when they changed their mind.
Smash 4: 2nd only to Sonic in 3rd party requests, it was only natural Mega Man would come in for the next game in the series. He was much requested 3rd party that had more to do with Nintendo overall then Sonic did. But getting Sonic in was a priority simply for the ol' Rivalry days in the 90s. Other then Mega Man though. Smash 4 was definitely kind of lax on the fan request portion in terms of newcomers. Not that any of the newcomers other then Mega Man or Little Mac didn't have ANY demand at all they just definitely were in a direction that didn't quite meet too many longtime fan favorite requests. Even in DLC, Cloud (Cloud was cited by Sakurai to be the most requested Final Fantasy character despite the lack of Nintendo appearances by the character and his game) and the return of Mewtwo, Roy, and Lucas was any inclusions for the fans that missed them. Mewtwo particularly since he was practically demanded right in front of Sakurai
Ultimate: This current game however definitely seems to have gone the exact opposite of Smash 4's focus where it is indeed taking fan requests for the most part even just starting with every veteran ever back. Maybe you can argue Inkling wasn't (Albeit that seems to be an example of a character both pretty well requested and just so happens to be a hot new IP that Nintendo cashed big on quick) and Simon maybe (Though he's always been a suggestion as an alternative to Snake and/or Bomberman. And Ryu's inclusion in Smash 4 drew a path for more then one 3rd party franchise per company. Maybe Simon did better in the ballot then we think. We'll never know for sure though) all the characters in Ultimate probably did do well in the ballot in some way. Ridley and K. Rool both having been amongst the most popular suggestions since Brawl. With other Brawl followings such as Geno and Skull Kid being now considered quite likely now (Whether that bears fruit remains to be seen). And even the echo fighters one way or another were popular requests.
Nearly all the games since Melee have paid attention at least somewhat to what fans have wanted, it's Ultimate however that has definitely catered to fans more then any other. So it's definitely no surprise that the chances has shifted mainly to characters we know have been long requested. There will probably be another case or two of a more Smash 4-like inclusions such as a Gen 7 Pokemon. But otherwise the majority definitely seems to be amongst characters that have been much wanted.