ATC won't ask for an expeditious take off. It's normally up to the crew to request an intersection take off. Normally if it is the first flight of the day, we use full length to give the engines time to warm up properly on a cold winter's morning.
It is company policy to use intersection takeoffs as far as possible as it saves unnecessary taxi time, as well as extra brake usage. Intersection take offs are not allowed during low visibility takeoffs when Low Visibility Procedures (LVP's)are in force. For a wet runway, it generally is also not allowed.
What's gets me sometimes, especially in Cape Town is one asks for an intersection take off from ATC. They give it to you and sometimes you might end up waiting at the intersection holding point for some time if an aircraft is on final approach. Knowing this, they often won't alert one to the fact that there will be a slight delay, and would one not prefer full length instead. JNB ATC have caught onto this, but not Cape Town. I now say "Request intersection XXX, if no delay...". It seems to help a little. Cape Town ATC don't understand its pointless using an intersection if its not going to save you any taxi time. Any Cape Town ATC's to comment...