I wish they'd just make placements one game like it is in Starcraft. People have this false sense that placements are a soft reset and you get to prove to everyone you're actually a GM+ level player by going 7-3. When in reality you were just playing against often times worse players than you normally play against. You never played against Master level players in the placement. You don't deserve to have your SR skyrocket because the season ended and you feel you deserve a higher rank. You are what your league icon says you are.
I think we can all agree people get placed fairly accurately, no matter how much people think otherwise. So really the issue is how to make competitive more engaging/fun.
For the most part, only way to do it is add more carrots. Carrots can be additional rewards, additional breakpoints, or a combination.
Again, looking at the League of Legends system, I actually think that would suit OW even more perfectly than LoL.
In particular, the "League" system in LoL is pretty pointless in LoL, but in OW it could be awesome. The 3 month refresh is desirable for it, especially if there are rewards attached for placing 1st in your league.
For those in the dark, LoL puts people in artificial "leagues" of ~100 players. Nobody ever looks at their league or cares about the standings because there are no rewards and people are just trying to rank higher, and since LoL seasons last an entire year, everyone is hoping to advance.
In OW the 3 month reset means you can keep people in their "placed" league, and depending on their finish, maybe next season they join a league 1 tier higher, or lower. Reward loot boxes for placing high in your league, etc.
2nd thing LoL does is breakdown the divisions into 5 tiers. ie: gold I, II, III, IV, V. Gives people more feeling of achievement when progressing.
Might be less desirable to have this in OW though since games are so much faster you'd end up bouncing through several tiers every play session. Only way it works is if it was more of a grind to advance/fall.