Imagine a situation where you own a house and a piece of land it's built on. You estimated the value of the whole thing to be $500k. One day someone knocks on your door and offers you $2m all of a sudden. Will you sell or suspect they know more than you? Maybe there's an oil deposit underneath your house? Maybe there's geothermal energy source? Maybe an international company has plans to build a facility nearby and will need your land for whatever price?
I'm asking this because if the funds get approved all at once there will be a large pressure on bitcoin's price and supply is, as we all know, limited.
Nobody buys bitcoin to sell it cheaper, so if they offer you $100k, they think it will go higher. If they offer $1m it's again going to go higher according to them.
Will you simply give it away once someone hands you $100k, or decide that it's cheap and they know more than they're willing to share?
So you are trying to compare Bitcoin to a house? This comparison doesn't work me. My house is the place where I live. I'm emotionally attached to it. It will be really hard for me to sell my house, even if someone offers me a great price. I'm not emotionally attached to my Bitcoins, so there won't be any problem for me to sell my BTC at a bull run or even at ATH, because I know that bull runs are followed by price corrections and bear markets. I will most likely sell BTC at a bull run and buy back at a bear market.
There's no way Blackrock to offer me to buy my BTC in the real world. Big institutional investors simply don't work that way.
Blackrock might offer me to deposit my BTC in their hot wallets, so that they could "manage" them for me.

I would never agree to such thing.