"But wouldn't that affect every site we're trying to use?"
No, only those that take a route through the bottleneck.
"And would that explain so many people experiencing the same problem right now?"
Yes, if they are all routed through the bottleneck.
"I have to concur, Ancestry's servers seem to be inadequate."
If you concur, you are only agreeing with others who share your lack of understanding:-)