The Fed has also said that they don't want to influence market share of ETFs so that's been interpreted as some sort of benchmark per manager. I believe Blackrock was around 50% of qualifying ETFs outstanding at the time. The Fed published purchases to date last week which has a pretty decent breakdown: https://www.federalreserve.gov/monetarypolicy/files/smccf-tr...
Also, the Fed has not purchased a single corporate bond yet so the "majority of the money" has gone to ETF purchases so far; the vast majority of the facility's capital is currently sitting in Treasuries.
The mere announcement of investment grade ETF purchases re-opened the primary markets without the Fed spending a penny. High yield primary markets were completely shut for a week before the Fed said that they would purchase fallen angel bonds and HY ETFs. The whole purpose of these facilities is to make sure funding markets function properly and ensure that companies that would have been fine without the pandemic will be fine now; not bail out distressed companies that are going to go out business anyway.
I don't even know what you're talking about with bank failures on this. The Volcker Rule really gutted bank prop trading and banks barely have any of this stuff on their balance sheets. It's a big portion of the reason why there was a massive lack of liquidity during the first quarter of the year.
Additionally it’s important to look at how the ETFs work. I believe the ETFs in question here are LQD and HYG for investment grade and high yield respectively. These ETFs track the iboxx indicies for IG and HY. Even if the Fed is buying BlackRocks ETF, this bolsters the prices of the individual bonds, which then moves indices higher, thereby also moving up other provider’s ETFs along with the entire fixed income market. Given this is the case, one should pick the most liquid ETF for each asset class (Ideally all ETFs should be purchased weighted by the NAV or trading volume of each ETF), in that case it would be BlackRocks for US fixed income.