It's why I'm picking Goldman over banks like ally or synchronicity, because I've never heard of them and wouldn't trust them, but I'm still not convinced.

Well if that's your reason, GS is actually the newest entry into this market out of these three as they didn't used to have a savings banking arm before they acquired GE Capital. Ally, which was formerly GMAC (General Motors Acceptance Corporation), has been around since 1919 and is in the top 20 largest banks in the US by assets. Of course, you could've just Googled this.

But what we're wondering is whether the hassle of dealing with an online bank over the phone or online

The only difference is they don't have physical branches. Phone and online customer support would just be like that of any other bank.

Can you clarify what exactly it is that your afraid of? Like a specific scenario perhaps? It's not like you're going to withdraw $100k out of an ATM. If you were writing a check, you'd need to transfer it to your checking account anyway, which you can do just the same from an online bank account (takes about 4 days if your account isn't at the same bank, just like any "traditional" bank)