One example springs to mind. I bought some ETH once they initially began supporting it, just before it shot up in value. However, the transaction just seemed to disappear and I lost out. I tried contacting support by they just kept closing my tickets without explanation. Very, very frustrating.
I know a story when someone bought some coins with Visa credit card and they had some issues with Conibase service. Same story with tickets - open only to have it closed down next day with suggestion to look into knowledge base.
Then they proceed to the bank and opened a chargeback dispute based on false advertising (legitimate reason) that Coinbase promised to help and are not.
You see - since crypto-currency is not tangible item (you can call it service, if you will), neither Visa, nor Amex or Mastercard will have issues with your dispute, because there is even no tracking to proof you received your "product". Of course once the funds are returned to your credit card and bank notifies Coinbase about the dispute, Coinbase will take your coins away from you, but that's not the point. You see -- it doesnt matter to Visa if you process $1 billion in monthly transactions - if you have too many chargebacks, they will shut you down. End of the story. You open another account - you go on the MATCH list and owner(s) SSN/IDs are on it for 5 years so bye bye processing credit card transactions.
Coinbase might not care about you (I am sure they do per se, they just cheap and won't hire enough eyeballs to answer customer support), but surely they care about their chargebacks dispute level.
That said I'm currently experiencing a problem where all emails from Coinbase to my email address are being lost and it isn't a spam filter. I emailed them describing the problem and they emailed me back with the boiler plate suggestions about checking your spam folder that can be found on their support website. Which I explicitly said I had already tried in my support request.
If all they are going to do is regurgitate information from there website why do they have support people at all?
If anyone from Coinbase is reading this all email sent from Coinbase to the Purdue Alumni email forwarding service @alumni.purdue.edu is being lost or not sent or something. It may have something to do with the fact that the alumni.purdue.edu server doesn't support TLS. I don't know just a guess but I know something changed in the past couple months and I don't even get marketing emails from Coinbase any more and it is preventing me from logging into my account.
I had a similar issue. I posted a clear support ticket, heard nothing for at least a day or two (probably longer) then got boilerplate about checking the support website. I replied saying I did and that the information on the support page couldn't be used to solve the problem. Nothing from Coinbase for a week, then another bot email saying they'll close the ticket unless I reply (again!) saying my issue was not resolved. This back and forth lasted over a month.
It reflects pretty poorly on them as a company and I really can't recommend using them as a result. The underlying support issue was related to their verification software. If their verification software doesn't work for some reason and their support is isn't focused/careful, then you're out of your account for more than a month.
Don't let centralized authorities keep your private keys.
But for the average person the chances are much higher that they will get hacked or lose their keys than losing their coins on Coinbase.
There are several important differences between Bitcoin and traditional currencies. This may be the most important one to you, but it is not to everyone.
That said, I also don't care as much if those get hacked as I can recover from stolen identity, while it's impossible to get back stolen bitcoin.
One week after contacting their support and not getting any response, I got an automated response asking if I am still interested in a follow up and if so, I should reply to this mail.
This continued for 2 months every week. I then decided to start complaining on their subreddit and twitter and coincidentally immediately got a mail helping me with my original problem and finally fixing it.
Now with the hardfork I withdrew all my funds as well and will never go back.
So I don't trust them and as soon as a viable alternative comes along I'm off Coinbase.