I can only pass this on from a New Zealand point of view but;
We looked at doing private work in conjunction with our Council duties but we decided it wouldn't sit well with local private contractors or ourselves. It also proved way to complicated to work out how to operate and our main concern was to provide the rate payers a service. We have more than enough tree work to keep us occupied.
Council equipment is budgeted for in capital expenditure just like most arb companies. We didn't get the best of equipment and we certainly didn't get the worst. Often, where it falls down is with wages. We have a set pay structure which isn't based on industry rates but, rather, a an internal pay scale. This means that we no longer attract the best arborists. Also, it's council and arborists tend to know they won't get the cream jobs like they would at an outfit which is solely dedicated to tree work.
It's not just Councils who can cover the costs of over runs elsewhere. I know, and have worked for, several large tree outfits who are able to "hide" private contract over runs on other large contracts including state owned assets that are being paid for by the tax payer. It's easy to hide a few hundred bucks on a multi million dollar contract on a very regular basis. Auditing is very rare and those doing the auditing really have no idea what they are looking for.
From a personal post of view and in regard to the lax attitude of Council staff; I can honestly say I spent years trying to encourage a private entity mindset when it came to production and work ethic but eventually, you get beaten down. Ive spoken to many ex and current council employees and they feel the same. Most don't come to council with the intention of doing naff all but it really does become a case (eventually) of monkey see monkey do.I know staff who have been at Council for over 25 years. They know it's a cushy number and they know how to play the game. My private work is what keeps me sane. In fact, I'm considering giving up the cushy, well paid lifestyle because I miss the hard work, the interaction with others who actually know what they are doing and being able to run a job from go to whoa.
There is also the issue of having Managers that have the council mentality ingrained in them as they have been there that long or have never worked in private industry. Managers and supervisors that have been put in the position without having the necessary qualifications or knowledge or skills to be able to do the job (there's a phrase for it but I forget). Very often in the arb industry, you have managers, supervisors etc who have come through the ranks or, in some cases, business managers who are just that and leave the day to day running of operations to those who know what they are doing. Unfortunately, in council, this is often not the case so everything is controlled by a person who knows nothing of the industry. That includes time frames, processes, finances etc. It is very easy for subordinates to "manipulate" managers as the managers have no idea how long a job should take, costs, etc.
Under H&S law in NZ the PCBU (person controlling a business undertaking) is now in the gun if a workplace incident/accident takes place so council spends a lot of time and money making sure that they have systems and procedures in place to cover the organisation, CEO etc. We get the usual BS about wanting everyone to go home safe but you can read between the lines with some people. Plus, less accidents equals lower ACC fees in NZ which can be in excess of $1 million.
Ive waffled quite a bit and some of it might not make sense in relation to the OP but I'm happy to answer questions I can.