I don't think Bakkt will directly influence the price of BTC at all. However in the future when bigger players want to dabble in crypto, say as the next bull run comes, then they might want to be able to use Bakkt for institutional plays. That's when it will indirectly increase the price of BTC.
It will directly influence the price of BTC since they are trading Bitcoin backed futures (meaning they can give or take certain demand out of the Bitcoin market). But to what extent is still unknown. We see BAKKT is still on its intial stage of gathering clients, so we do not see any substancial effect of it on the market. I think we a bit of patience to see the actual affect of this platform to the Bitcoin industry.
In my opinion Bakkt will affect the price of bitcoin. The price of bitcoin will experience a sharp increase. Because Bakkt is a crypto platform created by large and trusted companies and this has the potential to attract large capital to the crypto market. The demand for bitcoin will increase and prices will increase.
Majority of the users believed everything that has been stated by you will take place by the launch. To the expectation it hasn't gained good support. Less than 100 bitcoin got distributed through the futures contract. Some play has been performed to outlaw the progress of Bakkt. It is a very early stage. Hope things will change slowly when the market slowly recover from the immediate drop.
I believe Bakkt had been accumulating on its early phase, so when it launched the Bitcoin needed is ready to fill the demand of their initial clients.