COLA I would say has a negligible impact on the insurance rates (I could be wrong). It's more income vs claim payouts that contribute to rate increases. Also, regulations that require insurance companies to carry specific cash reserves to pay potential claims (so they don't go bankrupt after a natural disaster,etc.).
Rates often roll in several year cycles. Rates are low while they capture new business but claims start biting into profits thus rate adjustments begin to occur. It's not a bait and switch, as insurance carriers are so large they are not looking at each policy individually (even driving records are not always looked at every renewal). It's all mathematical models determining what they think they should charge based on potential risk.
Driving record and annual mileage are key factors. Lots of factors go into developing rates per each vehicle, repair costs etc.
The agent may be able to make some minor adjustments to save your $$$ like adjusting annual miles. However, your best bet is to see what company is hungry this year for market share and switch. Or go through an independent insurance agency as they often have numerous companies they work with.
Probably too much info but I wrote home and auto insurance for over 10 years....