Can you define "well respected" in a bit more detail? It seems that by definition, everybody in the cryptocurrency space is still fairly new at this, reputations can be built quickly, and identities are less transparent than elsewhere.
There is a lot of shady business going on in traditional banking, but I can be reasonably sure that e.g. Deutsche Bank is not just one guy keeping all assets on his personal laptop who may or may not have died in India last week.
As for "outsourced", I thought that was supposed to be BAD? "Not your keys, not your coins", wasn't it? "Insured" by whom?
Whatever well respected means to you, there is probably someone that meets it.
If you like old guard financial entities, Fidelity has a custody service.
If you want an entity that has been in the space almost as long as Bitcoin and has never been hacked, Coinbase has a service.
If you want star power, Gemini from the Winklevii is your bag.
If you don't want to be asked a lot of questions and don't want to know a lot about your counterparty, I bet Bitfinex will be happy to help.
All of these (except the last) are insured and bonded by respected old guard insurers. I assume the insurance contracts are all written on fiat terms, so take them at whatever value you will. MtGox proves the usefulness of contracts imposed on crypto but adjudicated in fiat.
Of course, if you are an old school cyberpunk, you custody your own coins using a layered security approach designed and implemented by yourself. That sort of cowboy behavior is frowned upon by the SEC, so not really applicable to a public company. I would be surprised if Michael Saylor (the CEO) didn't self-custody at least some of his personal stash. Good luck getting him to talk about it though.
Bitcoin is growing up. It is being integrated into the existing financial infrastructure. The beauty of Bitcoin is that you get to choose how much you interact with these new on-ramps. If you want to stick to the anarco-capitalist foundational philosophies, more power to you. Literally, you retain more power in Bitcoin than fiat.
Don't expect the existing financial world to bend though. It will slot Bitcoin into the existing architecture and keep on keeping on.
There is a lot of shady business going on in traditional banking, but I can be reasonably sure that e.g. Deutsche Bank is not just one guy keeping all assets on his personal laptop who may or may not have died in India last week.
As for "outsourced", I thought that was supposed to be BAD? "Not your keys, not your coins", wasn't it? "Insured" by whom?