Their participation brings increased liquidity and market stability, potentially paving the way for a more sustainable growth trajectory.
I'm not so sure about this part, although we still don't have enough data for a better conclusion. But theoretically these institutions bring in large amounts of money in bulk and they could actually cause bigger swings (higher volatility) by their entrance and possible panic exit in case their company goes down or is shut down by the government or things like that. This kind of "shock" to the market creates more volatility not less specially since the regulations around the world are not yet solidified.
That's right - we have some prior evidence. When Elon Musk announced that Tesla was accepting bitcoin as a means of payment and he invested in it - then the price of bitcoin continued to increase and became more expensive. But it was when Elon Musk started talking about his desire to no longer accept bitcoins - that's when the panic set in and the price of bitcoin took a pretty dire dump.
It is difficult to achieve market stability even though institutional investors have entered. They can sell their bitcoin holdings at any time regardless of the reason - that will of course make the market fluctuate wildly. Whoever the investors are - they also want to profit even though on the surface they support bitcoin.