"Initially" only on mistakes
That's not necessarily true... I will clear you "initially" to FL 310 when I know your requested is further up but I cannot "now" because of traffic. I use the "Initially" to inform you that you can expect further climb within my sector.
If in an occasion you were cleared to a certain level but then had to be stopped for many possible reasons, some being; not giving the expected rate to get above traffic we've been monitoring you against or a change in situation where the opposite descending going down faster than expected and that the crossing will be more efficient at different levels, *cough* a cock-up *cough*, you will be told to stop climb "initially" so that you know you can expect further climb.
That "initially" most of the times gets rid of the "climbing FL310, however our requested today is"
some use it others don't, but those that do don't necessarily do it on mistakes.