It's not necessarily privatisation that does it.
Here in Canada my enhanced CRB equivalent is expected to take 4 months, though a colleague (ex- RCAF SAR pilot) has been waiting a year, and he can't even enquire why, as the procedure is classified and, yes, he doesn't have a clearance yet.
But I can get a Firearm in 4 weeks.
And a building permit in 4 minutes.
All are Government run; just depends where the cuts fall.