1. Iirc ROB actually does have invinc on grounded up-b, straight outta brawl, it's like 4-5 frames. But you're right that his OoS options are definitely subpar. Anyone smart enough should know they can CC usmash out of shield if they bother to space that close, and ROB has no other threat up close out of shield that makes CC a bad idea, only grab which doesn't care either way. His OoS options are great with a gyro, but I don't feel like the solution to ROB should always be "hurr durr get a gyro" because it's really not that simple.
2. His recovery is fine. It's got a huge distance and a lot of options, especially for stalling and shooting at edgeguarding opponents. Being really susceptible to gimps and mostly following a linear recovery path is a fair trade-off, for sure.
3. ROB isn't really lacking kill power. Usmash kills spacies off the top at 110 percent, with good DI, and can be combo'd into out of dthrow very easily.
On floaties, they'll die off the top around that percent from Nair, and much earlier from usmash.
Bair also kills well because it sends at a low-ish angle, and will set up for edgeguards at low percents... if you can hit with it.
You shouldn't be relying on fsmash that much, it isn't very good. It's very disjointed, and can hit opponents hanging on the ledge, but it doesn't have a whole lot of knockback and the hitbox only lasts for 2 frames. Beside ending dthrow CGs on spacies with it (and I think bair might be better for that purpose anyway), you'd really only get great results out of it at either very high damage, or near the edge to set-up for edgeguarding, or to cover options on an opponent who has to up-b to the ledge.
Remember also that ROB can and should be going very heavily for gimps as well. Fair is basically jiggs fair, uair is basically falcon's, and he's got three boosts+jump, so he can go out, cover a lot of options, smack the opponent out the blast zone, and still recover.