What I think happened: Old teams had their MMR hard-reset, but each player's individual MMR just got soft reset. So if you use an old team you get placed based on new MMR, while if you make a new team you get placed based on the sum of your combined individual MMR.
Example: My team was high Diamond 2 last Season. We went 5-0 in placements and ended up in Silver 1. After that we got like 35 LP per game and after a few games we skipped from Silver 1 to Gold 5, and then a few games later from Gold 5 to Gold 3. Next we'll probably skip from Gold 3 to Gold 1, though at this point matchmaking is kind of strange.
So, if you think you got placed too low, you could make a new team. If you're actually at a Silver/Gold level and are bummed about all the former Platinum/Diamond/Master/Challenger players facing you, well... I suppose you could wait for a bit, though statistically you're more likely to face other Gold players than Platinum/Diamond/Master/Challenger, I suppose.
Why did Riot hard reset old teams? I don't know, perhaps to prevent team selling?
When you say that "completely new teams were easily hitting Diamond1 from placements", you mean new teams with Master/Challenger players, right? People who previously didn't play 3v3 didn't get Diamond 1 from placements, right?