The phrase "any insistence" is correct and usable in written English.
It can be used when referring to a demand or request that is being made, often in a context where the insistence is being questioned or considered.
Example: "Despite any insistence from the committee, we decided to proceed with the original plan."
Alternatives: "any demand" or "any pressure".
Earlier, in Europe, Deila's team were embarrassing in a direct contradiction to any insistence of improvement.
The chairman of Countryside Properties, Alan Cherry, has already gone on the record claiming that any insistence on larger rooms "inhibits designers to some extent".
Any insistence on political correctness in public discourse is fraught with danger, regardless of whether it emanates from the left or the right.
You might hear the shadow influence of second-wave Detroit techno on "Speak the Name" and "Beat the Ground" in their asymmetrical pulse patterns — but you don't notice any insistence behind the allusion.
Other internal Syrian opposition groups, given consultative status at the talks, said any insistence that Assad should stand aside will be a recipe for a continuation of the violence.
The perception of Reed as a cynic or doomsayer is misleading; the only thing that truly enrages and frightens him is any insistence on cultural uniformity, or, to use a more sinister word, purity.
Some practical difficulties remain, including an insistence from Finland that any new loans to Greece should be guaranteed by collateral.
There is no widespread call for a critical eye to be cast over what is being done in our name, nor is there any organised insistence on accountability.
Lawyers in Brussels are no doubt hard at work trying to find a way to ensure that, at Cameron's insistence, any deal is legally binding and "irreversible".
On the other hand were the battered emotions: the ardent vows to not support Sen. Barack Obama under any circumstances, the insistence that every insidious rumor concerning the Illinois Democrat was grounded in fact, the belief that the party itself had conspired in an effort to tear down the Clintons.
The insistence that any effective monarchical rule must be intensely personal had obvious potential dangers.
