Could efficiency improve? Yes! But note that waste was private companies padding out the contract not government employees. People want to outsource government functions, blame government when that fails, and use it to justify increased outsourcing. Clearly there is a failure in that logical reasoning.
I have no references to back this theory up, but I feel like this is where most of the waste happens.
[Gov spend public money] -> [pay private company]
The government isn't incentivized to get the best deal for our money which results in overpaying or just flat out corruption. eg. I'll overpay my friend's company and they will kick me back some money for choosing their contract.
Is it that wrong that the people who ran one of the largest infrastructure programs in the US live in nice homes? The project was horrendously over budget and late, but it did do what proponents wanted it to do. Private firms taking over the commuter rail like Keolis don't seem to be achieving any quality or cost benefits.
We may be in a strange situation where fundamentally underpaid workers find ways to game the system to make about what they could in the private sector, would higher wages help eliminate the "wasteful" practices?
Have you seen the Big Dig? Look at the size of the check we wrote for that one. Now look at the kind of houses all the people who got to work on that project (whether in the office or in the field) in their mid and late careers (when you can make real money rather than be schlepping supplies around a job site for a "you haven't put in your time yet" size check) are living in.
Waste like that is why nobody wants to increase taxes. Pretty much anything more than the bare minimum seems to just slowly evaporate. The money goes poof before it trickles down into programs, infrastructure and services that actually provide benefit to the taxpayer. People would rather ride on a crappy T and pay marginally less tax than pay more tax to ride on a crappy T that has a handful more spots in the org chart for politicians to fill with people who won't show up.
Look at the semi-annual (well, let's be fair and give them credit, it's more like 3yr) state police "fraudulent overtime" scandal. It goes way, way back. Remember when the Probation Department got caught paying salaries to political appointees who didn't show up and didn't have any job duties? Remember when there was that enforcement/compliance arm of the Dept. of Elder Affairs that didn't actually exist like it was supposed to because the money was redirected to pay for more (politically appointed) middle managers who just forwarded emails all day? This is what "raising taxes" looks like in Massachusetts. For every $10 spent you'll be lucky to have a buck actually be used to run a bus, patch a pothole pay for healthcare, etc. etc. It's no surprise that people don't wanna pay for that.
People will pay for public services. Nobody really cares whether the garbage truck driver gets his pay stub on private letterhead or government letterhead. Nobody really cares whether they have public or private EMT services so long as they show up with equal promptness. What people won't pay for is public leeches and Massachusetts has done a very good job cultivating the perception that you can't buy one of the former without getting ten of the latter in the deal. No surprise that people don't wanna take that deal.