I'm honestly not sure where the base stats came from...I didn't mention anything like that. I don't know how Riot decides base stats and why certain champions have lower ones than others. I'm actually a little unsure of how to reply because it feels like that came out of left field. Are you saying that you think melees don't have enough base stats to make up for the range that marksmen/mages have? If that's the case, then perhaps the answer is simply buffing up some base stats instead of overhauling the whole game. It could just be a problem that fixing a few numbers could solve. Mind you, melee classes (outside of Juggernauts, which are specifically supposed to have kiting as a weakness) haven't had their class update yet, while Marksman and Mages both have had theirs. It could simply be that the class update for divers and bruisers will fix all your issues.
But mind you, marksmen and mages do have some inherent weaknesses that melee champions can take advantage of. For example, most melee champions I know of have either A) a gap closer or B) hard crowd control to make up for their lack of range. In most cases, if a squishy gets hit by any of that, they're typically dead. In addition, most melee characters have either A) tankiness or B) some manner of protection in order to stop themselves from getting killed at range (examples of this include Tryndamere's ult, Fiora's Riposte and Yasuo's Wind Wall). Most mages and marksmen also lack mobility or an escape, so they're screwed if they get reached. That's a weakness that they can mitigate, but melees can also mitigate their own weaknesses too, either with items or powers in their kits. Again, some people do deserve buffs or nerfs (looking at you, Jayce), but that's a case-by-case basis. Some melees could use buffs, some ranged can use nerfs. But overturning how damage and CC works just to make melees more viable is not really a good answer.
So you want melee champions to be more popular than ranged champions, in general or just in top lane? Because I can understand wanting melees to have a place in the meta that isn't overshadowed, but I also don't want them literally everywhere because everything else is unplayable. I get that it's frustrating losing to a Jayce, Kennen, Quinn, hell even a Teemo in top lane, but it's perfectly possible to win those lanes with a melee champ. I've seen it before, I've been on the receiving end of it before, too. I still have PTSD flashbacks about getting my ass handed to me by a Darius as Gnar. AS GNAR. Before he got super-nerfed. If someone knows what they're doing with their champion, and knows what the enemy champion is capable of doing, then winning is completely possible. Breaking the game just so melees can dominate isn't the right way to do things, even if it's really tempting to dumpster some annoying champions. It shouldn't be about a popularity contest.