Define what you think a fighting game is. Then see if Super Smash Bros can fit under those parameters. That is how you decide whether something is part of the genre.
You don't look at something and then decide to classify it, you make the classification and then see what fits under it.
Most definitions of Fighting Game include Smash. It has other "tags" as well that make it more than other Fighting Games. I'm sure someone could come up with a definition that doesn't include Smash, but it won't be the most common one.
If Smash started playing just like Street Fighter, Tekken or Dead or Alive with the next game, you can be sure that Smash fans will complain that its been made into a fighting game.
No, they'll argue that it was made into a traditional fighting game.
Your assertion is simply incorrect. ---
"I'm not racist but, BLM sure did make me racist." -Skasa I'm just here to offer you advice, take it or leave it.