I feel point 1 is a more specific example of point 4. Point 3 makes sense because banks are handling peoples money, I don't know enough about point 2.
However point 1 & 4 is more about market power than anything else, point 3 is more about ensuring confidence in basic financial services aren't undermined by risk taking which feels like a separate point.
Sometimes for reasons other than foul play or a poorly design regulatory system, there's value in an organisation being large as it has increasing returns to scale, it can produce more output with the same input compared to smaller organisations. It's also unfortunately one way how monopolies form, easiest example being utility companies because there's also a case not to break them up as well as they can provide the service at a cheaper cost, but will they? Which makes the problem harder to solve then just breaking these firms up.
In NSW Australia (New South Wales the state Sydney is based in), the problem was approached by creating an institution called IPART which basically determines prices/rates for both public and private monopolies. In Sydney there are private motor ways and tunnels, IPART determines the rates, and the water company (Sydney Water) largely has its rates also decided by IPART, same goes for council rates (tax on land/properties, etc). IPART is far from perfect, it answers to the Premier (the Governor) so there's a risk of it becoming an instrument of popularism, but this means Sydney water is chronically underfunded (and water rates aren't even that high), this has second order effects like Sydney Water dragging its feet on committing to providing infrastructure. There are massive fixed costs with starting a water utility firm so it impacts stuff like residential construction reducing overall house supply, which is a problem in Sydney when housing is so expensive.
Sometimes these larger entities form as a result of government created entry barriers, in America it's easier to get small business funding than it is in Australia. Also in Australia we have laws about prohibiting pharmacies opening too close to each other, which is incredibly dumb. There's a very strong Pharmacy lobby, not big pharma but instead drug stores which might be a uniquely Australian phenomena. But it means there's no drug store near my local train station in an area that was recently redeveloped, or a single Pharmacy in areas like Sydney Olympic Park, but 10 in a smaller older area such Granville.
In Australia we have 2-3 large grocery stores (Coles, Woolworths and to a lesser extent IGA), a 4th exists to an even lesser extent but has struggled to grow and has been struggling in part due to the land planning regulatory framework. Most cities in the US have something similar, but in NSW it's in overdrive plays a big part in why housing is so unaffordable as it largely determines how much floor space is allowed on each lot and how tall buildings can be. But back to groceries, it's very difficult for ALDI to get permission to build as many grocery stores to compete due to energy barriers imposed by the planning system. If you own the land, you need to first get a planning proposal in to rezoned and planning controls updated, then you need to make a seperate development applicaition which can easily take 5 years.
I believe parking minimums in the USA can have a similar effect, as many cities require different levels of free parking for different land use.
Sometimes over regulating things can result in a lack competition, and it's not always a result of a lack of government intervention. And sometimes there's value in allowing organisations to be large. And when it is a problem sometimes the solution isn't always break them up.