Not necessarily. If someone has the self discipline to throw all of that money into one account & still manage it then so be it. If not, then separate it into different funds.
I guess at this point we're really just arguing over semantics. I agree with you that it can be fine to have that money piled together, but then don't say that you have a $30k emergency fund if you're willing to spend $10k on "wants".
I actually do this in some ways with my credit union. They offer high-interest checking on the first $X dollars in your account; so I never let me checking account go below $X unless it's in the case of an emergency, and keep the rest of my EF in a separate account.
In the OP's case it didn't really matter since they're doing well financially, but I imagine it could be a problem for someone with a smaller income/EF.
I think I may have over reacted, since the OP probably didn't need to hear my statement. But I think it was useful to get that point across for other people perusing the thread.