As someone who plays both for dances (contra, English Country) and plays at Irish (and occasional old time) tune sessions, the issue of "at speed" is different for the two situations. It comes down to "playing well with others." In a session, it's the other players, for a dance, it's dancers' needs first, players trying to accommodate them.

In sessions, there's the chance to play at 78rpm if you can manage it, and that's lovely if everyone is an accomplished musician. But that leaves out beginners through intermediate players for all but a waltz. If a session is meant to encourage all, a range of speeds should be part of it. In mixed ability sessions here, the person who picks the tune sets the speed comfortable for them.

For dance, a skilled caller guides the band to the right speed for a particular dance. I know that there are some tunes I could play moderately in a session, I couldn't yet get "up to speed" for a dance. Band rehearsals frequently start with slower pace to insure accuracy, then speed up the tune to dance speed. I've found, in doing this, that tunes I think I have down solidly and play fast, I've dropped notes or mixed up phrases, when playing it through more slowly. ( I also note that 80% of what I play, I have the sheet music in front of me, even if I know the tunes pretty well. Having the dots is a whole OTHER kettle of fish in sessions)

Having a few speed demons in a dance band can cause problems, as they push the pace to an uncomfortable spot, or spoil the sound. The same thing in a session discourages those who can't keep up.   

Joanne in Cleveland, off to a session at the Irish American Club, East tomorrow!