I like FR.
If I was rebooting it, I'd probably go back to a time just before the 3e FRCS, which lets me pick and choose the bits i like most out of that generally excellent product. You really need to get rid of all the 4th ed Spellplague stuff because so much of it was nonsensical, poorly detailed, or rendered useless a whole swathe of perfectly good regional sourcebooks, and turned the whole pantheon upside down in a manner that would have had long-lasting repercussions that more modern FR products contrive to completely ignore.
Aglarond is more interesting with the Simbul still around, Thay is more interesting with the council of Zulkirs rather than Szass Tam ruling the place (even though he is the strongest of them), and the whole Thayan Enclave idea was interesting too. The Zhentarim were never interesting, do what you like with those. I prefer Cormyr ruled by Azoun rather than Alusair and the throne of Tethyr still vacant, so I'll take the pre-FRCS iterations of those places, but i don't mind the city of Shade still hanging around, and the Thunder Twin plotline that was introduced in FRCS had possibilities, if anyone had bothered doing anything with it. The Chosen etc were much less prominent in the setting way back in the Grey Box from memory, I'd wind them back to that sort of level. There was a one-line plot hook in FRCS that i always wanted to do something with, about the semi-divine pharoah of Mulhorand romancing a Cormyrian paladin of the Red Knight with potentially large political/religious implications, so that stays. Obould and the Kingdom of Many Arrows stays too, that was one of the better 3e ideas. I'd keep the very-LN realpolitik version of Khelben who's split off from the Harpers and is running his own network, more plot hooks that way. And while I don't think Zakhara has any place in FR, I think i would try to use an updated/modernised version of the Maztica/Amn situation in some way that bites Amn (and possibly Helm) on the bum a bit. And I'd retcon the whole thing how the entire Maztican society was destroyed in the novels and the responsible parties defeated by boring NPCs before PCs could even get there.
Bane over Iyachtu Xvim (what bright spark decided one of the top 3 gods of evil in the setting should have an utterly unpronouncable name, I want to know...), and bring back all the little obscure minor godlings like Nobanion, Siamophe, Leira, Gilgeam, Sharess and so on that always got cut from later products because of page count. I don't particularly like Cyric, but winding him back impacts Kelemvor (who I do like) so I guess he can stay, though I probably wouldn't use him myself. Not sure about Myrkul, there's not really space for him with Kelemvor as the god of the dead, and he doesn't add much that someone like Velsharoon or Bhaal can't do. Also, I'd add more evil non-human deities (I mean, look at the dwarven pantheon - what a bunch of boring goody-goodies! Abbathor, you're weaksauce and you need to get eviler or make way for someone who will. And the halfling gods are even blander. At least the gnomes have ONE token evil god!). Asmodeus and the Raven Queen can feel free to leave, nobody asked for them in FR, and there's already several more interesting gods filling their portfolios. The Raven Queen is basically just gender-flipped Kelemvor anyway.
FR has always been high-magic and kitchen-sink (in a good way) so I don't think much extra explanation is needed about the origins of teiflings, dragonborn, or even owlin, warforged, or whatever else you want to add to the setting. They were either always there in some obscure locale, or they were created in one of the zillion lost civilisations or divine curses or magical accidents or bouts of archmage experimentation that happen in the Realms every Tuesday.