The FY2017 budget returned inflation-adjusted per-capita spending to that of FY2005, almost exactly. The state spending in inflation-adjusted numbers went up almost exactly the same percentage as the population increased. The only thing that's been cut in the budget has been the growth over the last decade.

Were state services in dire straits in 2005? Was calamity about to ensue then? Was the only solution to institute a sales or income tax, while simultaneously dipping into the Permanent Fund? 

Go look at the numbers for yourself. The Budget Reports by year are provided at the Office of Management and Budget's website https://www.omb.alaska.gov/ .