I just needed my last two statements (July and August) from Vanguard. I went online and for some reason, there is no July statement.
That's one of the reasons I always download a copy of my statements each month (investments, cable bills, insurance, checking, savings, etc.) and keep them on my own computer (with multiple backups). I know some people don't bother saying "I can just look online if I need it", but my experience has been like yours. Either I can't get access to the statements, or some are missing. This seems to apply everywhere, not just Vanguard. Plus, you never know when internet access will be down, either your own ISP or the server you are trying to connect to.
I used to scan paper statements and save them, so downloading an electronic statement is so much easier now...
I don't know if any other company is better. I'm generally pretty self-sufficient so rarely need personal help. But I think at this point, I'll probably move my brokerage account to Fidelity as well.
I've been with Vanguard since 2016 when I moved my IRA from my local bank. Like you, I tend to be self-sufficient and can't recall ever needing to contact Vanguard for anything. I have no experience with any other brokers, and so far haven't had a reason to switch. The Vanguard web site can be a bit confusing for some operations, but as long as I can accomplish what I want I don't mind. I'm still in the accumulation stage, so hopefully things don't become a problem when we start withdrawing for retirement.
In some ways, I like the old "Tried and True". Even if the web site is clunky at least I know how to get things done. My local bank seems to update their web site every couple years and I have to learn how to use it all over again. Their "improvements" seem to get more and more complicated, not easier.
If you have all of your other accounts with Fidelity, I would probably move the brokerage account there also. Just for the simplicity of one place to deal with if nothing else.
Otherwise, I wouldn't make a switch just for a single problem or two. All companies have issues and customer support sucks just about anywhere these days. Of course, if it becomes a pattern, then yes find greener pastures.