Yeah, the federal system for sure has that built in...actually to the point of being borderline unfair for the GS employees who spent their whole career in a high COLA area since COLA isn't included in the calc (but is for WG employees for some reason). But every time you see a headline about some ridiculous firefighter/cop retirement it's almost certainly a local jurisdiction that didn't close the loophole (but probably has now!). After working in the federal government and now working with some local jurisdictions it's interesting the range of professionalism you get at the local level. Some up there with the best of the federal government, but many just shockingly unprofessional and poorly run.
You are right. The problem is most municipals won't fund the pensions because they don't want to raise taxes and just kick the problem downstream for the next elected official to handle. I ran a simple calculation for someone starts work today at 20 and starts to receive the annuity at 65. Buys a defer annuity, with $5K invested every working year, adjusted for inflation of 3%, assuming he puts it in SP500 index. He will receive ~ $15,000 a month payout @ 65. That amount is equivalent to ~$4,000 a month of spending power today.