I'd be curious if you can point to a study that shows the opposite? Besides, individual worker productivity is not the metric that matters if comparing public vs private for some jobs. If a company is squeezing crazy productivity out of their employees but keeping a huge profit on top, it's meaningless to the taxpayer. Limited competition has become rampant in these days of worker shortages, too, with public tenders often now coming back with prices well above internal costing. I work in contract administration for tendered public work, and we're increasingly seeing either a single bidder well over budget forecast (yes, factoring for inflation) or obvious signs of collusion. When I was a contractor, collusion was rampant in that market as well. Ironically, the low-bid process actually encourages those shenanigans.
Saying all private is better is as wrong as saying all public is better. Each has its place. Private prisons in the US, water and electricity in the UK, and countless other examples, have had horrible end results for the public. Other privatision has been more successful, though it takes time to measure the results.
For example, they went private for garbage in 2015 in a BC city near Vancouver and it started out great as the market was flooded with competing outfits all desperate to build a client base with low prices. Over time, the competition thinned, the prices rose drastically, and the service quality dropped. Eventually, it was no better than it was before, and in many ways worse, so they have since reversed course and returned to a city-managed single collector.
When I did work on a Telus building in BC, the layers of waste and bureaucracy were eye-watering. Middle managers became professional problem-dodgers, avoiding making decisions and deferring desperately needed projects until they inevitably got shuffled to a different department, leaving the new guy to work out how to avoid the risk of making a decision and spending money. I still grit my teeth when I pay my mobile bill, but I know Rogers and Bell are just as bad if not worse. (And before anyone points to cheaper rates in the US, they have the same short list of players, just massively increased density and volume that keeps costs lower, not some magic privatization/deregulation formula).
My theory is the problem isn't inherently public vs private, it's a problem with massive organisations and the inherent LCD systems therein that create endless waste and inefficiencies. People I know who worked at Microsoft and Google noted similar bureaucratic incentives to delay, waste and obfuscate due to the sheer scale of the operation. When things get that big, agility is impossible and waste is inherent. Working with the City of Toronto is much more difficult and layered than working for the City of Stratford.