It's worse than that if the amount is non-trivial. Wells Fargo won't allow you to send an amount over $10k instantly without physically entering a branch.
While limits might not be much different from other banks, at the very least it's not Wells Fucking Fargo.
Seriously, do some research. I'd never use those fools.
When I lived in Australia, which I believe has a very modern banking system, I couldn't instantly send more than $5k a day. The one time I needed to send more money, I was fine with going into a branch.