Okay we'll compare their abilities. We'll also assume that Gragas is building tank and Janna is building utility AP, since those are the standard builds and you quote "without the need to build a single item to make it hurt." Janna's cooldowns are mostly lower by mid game as she likely has anywhere from 15%-35% CDR from items.
Passive: Janna grants move speed to allies moving towards her. Gragas gets extra health back in lane. He's melee though, so he'll likely get poked down a lot and will need that healing just to stay in lane. Janna's passive allows her adc and her team to kite more effectively at all levels by just running behind them.
Q: Janna's Q provides a knock up with a range of over 1700 and a duration from .25-1.25 seconds. Gragas' takes 1 second less to charge and has a greater slow over 1.3-2 seconds but significantly lower range. His base damage is higher than hers at all levels, but he builds nothing to contribute to ratios, which means that by late game they're about even. The barrels are also arguably much easier to dodge.
W: Janna's W gives bonus move speed and allows her to move through units when not on cooldown. This synergizes with her passive during all stages of the game. The active is a slow from 600 range over a duration of 3 seconds. Gragas' w is damage reduction in exchange for being unable to use spells or aa, and then does a small amount of magic damage plus 8% of their max health if he manages to auto attack.
E: Janna's E is arguably her best spell. It gives a shield with good ap scaling and base values that also gives bonus AD to whoever she shields. This skill is usually maxed first and gives the equivalent of a free bf sword at max rank. It can also be cast on turrets. Gragas' E is his main engage/cc, putting him in melee range of an enemy in exchange for knocking them up and stunning them for 1 second. By now we're realizing that all of Gragas' base damages are pretty high, but they also don't scale because you're building him full tank.
R: Janna's ultimate is a knock back that also heals minimum 300 health to any allies in its range over a 3 second channel. Gragas' is also a knockback with relatively the same area of effect and (you guessed it) high base damage. Also it's considered a projectile by Yasuo windwall and Braum unbreakable.
Range: Janna has an aa range of 475. Gragas is melee at 125. Janna's abilities range anywhere from 600-1700, whereas Gragas' are from 125-1150, decreasing heavily to a maximum of 850 after putting a second point in his ultimate.
The biggest factor here is range. Gragas is a very strong generalist jungler, and it shows with his high base damages, some method of sustain, and the ability to cc people as well as deal damage. However, his knockup, which is already inferior to Janna's in range, area of effect, and cc duration, requires him to be in melee range of his targets. I think you can hardly call it peeling when in reality it's more of a "take me instead" suicidal move. Most of the time a good Gragas body slam can be used to reengage, but we're talking about peeling away enemies for your carries.
His CC durations are lower. The cooldowns are higher. Everything has less range, and the only knockup requires melee range and almost certain death (Gragas isn't a second Leona, either). The ults accomplish the same kind of displacement, But Janna's comes with a heal while Gragas' does damage. If your role is to peel, than anything short of an instant nuke (they can't kill you if they're dead) is useless. A Gragas ult throwing off a Zed and taking away 200 more health isn't going to save your ADC when the death mark pops, but that same displacement plus an AOE heal just might. Janna's abilities and passive allow her team to constantly kite an engage comp, while Gragas' relies on getting a pick (a method of engage) or using his ult to end the fight before it starts and hope that your team will win it later.
One massive post later,
TLDR; Janna's kit has less damage, will actually scale with her build, and is designed to kite, peel, and disengage, which is her entire identity. Gragas is a generalist, which means he has higher base damage/cc values, lower cc duration, is also melee, and can be easily kited. As far as peeling goes Janna's ult is entirely more successful. Her kit provides constant peel, his is much more situational and arguably suicidal.
Again, it's not that Gragas support can't work. It just won't necessarily work well, and not as well as the leaders of individual niches. Thresh is the best generalist support, so playing Gragas support is a matter of personal choice and enjoyment, not any advantage that he brings to the table.