Paranoid is the new sensible

But seriously, given exchange and wallet failures over last 2 or 3 years, ANY site seems to have about a 10% risk of getting fucked, whether by mismanagement, incompetence, hackers, regulation, just plain scamming or whatever.

So yeah, wouldn't leave coin on any of them.

Keeping some of your coins in coinbase vault is a good idea if your not 100% sure about your offline storage solution, they should be safe from hackers there but government is another thing.
Have a look at something like Ledger or Trezor wallets.
Always a good idea to spread your BTC savings about a bit.
I always keep 70% cold storage, 20% Coinbase, 10% hot wallet or similar.

If the coinbase vault works the way they claim, you would actually be safe in that scenario.  (Because, if it works the way they claim, they truly don't have access to all the private keys necessary to spend the multisig funds.)  Unfortunately, unless you examine the javascript code being used every single time you use the site, you can't be 100% sure that it works the way they claim.  Still, I think it's *likely* that it does, and that you would indeed be safe in such a situation.

However, as others have mentioned, when in doubt, always assume the worst, and if you and you alone don't control your private keys, then the money isn't yours.

I don't use coinbase's vault, because I'm savvy enough with Bitcoin to know how to secure my own funds.  But if I wasn't as good as I am, and I simply didn't know how to properly secure my funds-- then ya I wouldn't know who to trust, and indeed that would be a scary situation to be in.  So my advice to you is to learn more about tech and security, so that you can know enough to be confident in your own solution.  However, until that point, I think it's highly probable that you can trust Coinbase's vault, because if it works the way they claim, which I think it probably does, then you are safe.

The government cannot actually "freeze" bitcoin assets as they would need the private keys of all addresses to effectively do this

They really cannot "ban" bitcoin either as it is something that can be traded in a p2p manner plus the various nodes can operate in ways that would prevent government detection.

Yes, but, think of what things will be like when they go a little further and schizophrenia is the new sensible.   

Here, You can find an explanation of Cold Storage. As I said before You could use for your cold storage a Paper Wallet.

 

I keep ALL my cins offline in my own private wallet that is not connected to the internet 24 hours a day so I have no worries about this. You can be sure if the US government ever did seize your Bitcoins. They would be selling them, HOWER they can not just seize them, a law would have to be passed, and they are not considered a currency so they have no legal right to seize them at all. If for a weird reason the US Government would recognize them as "Currency" or "Commodity" get your coins out of there, because at any time the US government has the right to Seize residents currency that could be related to terrorist actions. This includes USD, Gold, Silver, Bronze, platinum, or any other possible form of currency or commodity.

Why do want to keep there in the first place? Given the history on exchangers going bust, that would tell you everything. Unlike paper money where you can't just keep everything in your house, bitcoin is totally different. Create your very own wallet and have your btc accessed only by you.

They could crack the password like they did with some of DPR's coins, though if you have a ridiculously strong password this shouldn't be too much of an issue.

Yeah, that could work "Sorry Mr Fed, only my alternate personality has the keys and he only comes out in tropical countries with no US extradition treaties."