Every businessman, its target is to realize a profit in the end and that's the game that these institutions, Banks, or hedge fund managers play to try to accumulate their portfolios fast and at cheaper prices. From the institutional point of trading, their way of trading is slightly different from the way we the retail traders trade because of the huge amount of money that they have (Millions-billions of dollars), so it takes them some time to properly take their position in the market because they need liquidity to buy therefore they would employ various ways to get their portfolios ready, maybe buying via miners, the OTC market and even from the main market.

I wouldn't call this a "silent method" to buy BTC. This is just a direct method of buying lots of BTC by bypassing all the middlemen(centralized crypto exchanges). I'm sure that OTP trading could also have an impact over the Bitcoin price, because we can't have difference prices for Bitcoin on the trading platforms and outside the trading platforms(at least not in the long run). The miners also want to sell at a higher price.
The Bitcoin market cannot be controlled. We live in 2023 not 2013. Of course that the institutional investors are doing this for the profits. Do you think that they are doing it for charity?

it doesn't have to be miners. It could be other big traders who plan to close a position or market makers who make a big deal with the right premium and then try to close it in the market at a better price making money on the spread by providing the product to the whales - liquidity and time.

And I also heard a rumor that miner tokens are more expensive than market tokens because they are harder to track because they have no transaction history.

And back to the OP's question "are they doing it to gain control of a large percentage of the market or it is purely profit driven?"

What's the point of having a large market share if you don't make a profit? The goal of every investor is to book a profit at the end of the trade.

If they intend to gain control of a large percentage of the market, their ultimate goal is also profit. If they don't profit from controlling the market, what's the point of controlling? Just like why governments and banks want to control our money, isn't it because it makes them profitable? So I will agree with some of the above comments, organizations, governments or anyone once involved in investing in bitcoin, the profit is what anyone is aiming for.

It's going to be more about getting better fills with their purchase at the current and fair market price in my opinion.

About your hypothesis about institutions wanting "to gain control of a large percentage of the market" - I believe for entities like BlackRock, it's ALWAYS in their M.O. to corner the market, IF they can. The situation that we should be concerned about is, how much of the TOTAL SUPPLY should be STORED in THEIR centralized vaults before we can actually say that Bitcoin is failing? What is the threshold? 50%? 60%?

Well, Institutional purchases of Bitcoin, whether through OTC (Over-the-Counter) trading, can serve various purposes and it's not necessarily an either-or scenario between gaining control of the market and profit-driven motives. Here are some key factors to consider:

Profit Motive: One of the primary reasons institutions invest in Bitcoin is for profit. They believe in the long-term potential of Bitcoin as a store of value or digital gold, and they seek to benefit from its price appreciation over time. OTC trading with miners can offer advantages like lower fees and reduced price impact compared to buying on public exchanges, making it a more profitable approach.

Risk Diversification: Institutions often allocate a small portion of their portfolio to Bitcoin to diversify risk. Bitcoin's price movements are relatively uncorrelated with traditional asset classes, which can help mitigate overall portfolio risk.

Hedging against Inflation: Some institutions view Bitcoin as a hedge against inflation and currency devaluation. Buying Bitcoin can be seen as a way to protect the value of their assets in an environment of monetary expansion.

Regulatory Compliance: OTC trading with miners or other large holders of Bitcoin can help institutions comply with regulatory requirements. It allows them to conduct large transactions without causing significant market disruptions or raising concerns about market manipulation.

At last I can say,
while institutions do aim to make a profit when they accumulate Bitcoin, their motives are multifaceted. Profit is certainly a significant driver, but so are diversification, risk mitigation, long-term holding, and adherence to regulatory standards. Gaining control of the market is not usually the primary objective, as the cryptocurrency market is highly dynamic and difficult to control even for large institutions.

Look, Saylor's buying sprees during downtrends might seem like a coincidence to a naive viewer, but they're actually very smart! OTC trading isn't a dark, secret rite; it's a way for large institutions to hide their identities. It lets institutions buy a lot of Bitcoin without setting off alarms on the market

Why do they do it, though? Do you want to help people or do you want to hurt them? Both! Institutions aren't like simple picture bad guys or good guys. There's no doubt that they want to make money. But with money comes power, and power brings control. When you have a lot of Bitcoin, you're not just involved; you're a force to be taken seriously. And believe me, these places? They want to think deeply

Talking about this matter is more like a conspiracy because no one can verify it, we're just use our negative view against the centralized institution. I think there's always a clickbait news whether it's a good news or bad news, but it depend on which one will viral.

The most viral news will affect the market and people will not aware with the other news.

because they need to have reserves to prove they can open up a ETF market

they need to have the reserves to even be able to offer baskets of shares that represent the coins
they cant sell unbacked shares to then buy coins they do not yet have.. as thats against the purpose of a ETF

its why the winkle twins(gemini) grabbed loads of coins before filing a ETF many many years ago. its why grayscale did too