I was under the impression that semi-decent pushers like Jarvan, Ryze (pre-6), Kogmaw, Kassadin (doesn't usually go bot, but is perfectly viable with promote), Riven, etc. thrive with the ability to free harass their opponent without worrying too much about the minion wave. It's also useful on heavy pushers, but so are other summoners.
My experience is that actually those are more powerful than other bots for that reason. They can zone you, and then you have a giant promote guy, and if you dont have promote, you are going to be capped.
Take anivia. She cant fight those pre level 6, she is gonna be zoned, which is bad enough, but the promote will seal the deal SO FAST that anivia is a sitting duck. Anivia will lose bot 100% of the time against anyone with promote. I would say maybe even having promote herself.
But let's go claim by claim:
1. Less champs are viable.
Why? because many, specially squishy champs, Ap nukers and ranged ad, rely on Summoner spells to survive the jungle. If they have to use one slot for Promote it hurts them. So what's the solution? The solution is to not pick those champs, instead go pick one of the champs that can survive the jungle with out promote.
The reason Promote reduce the viability of champs bot is that it consume a summoner spell, imagine that you remove one summoner spell slot tomorrow in lol You know what will happen? the tier list will changes. Because a lot of champs lose viability, thats what promote does, removing a summoner spell, removing viability.
2. Someone without promote can stop someone with promote. Rarely true, incidentally for the same reason nekrogen said some champs are viable. Some champs can go and fight 1v1 and zone badly, in the meantime a promote is going to eat the creepwave, if you dont have the promote to let both big guys fighting, he can zone you and let the 2 creep waves fight and the one with promote will be win badly, before you know you have a huge unstoppable creepwave that is more scary than the opponent champ.
Again, I'm willing to try again anyone. The only way the guy with promote (guy A) do not overwhelm the guy without promote (guy B), is in a match where if both players had promtoe B would overwhelm A.
3) If you send the guy buck you put more pressure, promote or not, no reason to go help the ganker fight when you can VERY FAST take the point, specially if you have the promote.
Of course bot should go top or help mid fights etc if he is pushing well (which brings me to the point where champs that need summoner spells to survive those fights, are handicapped bottom by the presence of promote)
Edit: Yeah plz dont even talk about yorick, he is a broken piece that should be banned and not even worth talking.