This has been beaten to death in other threads related to this over the past several weeks, but the short answer to your question is "by putting money toward infrastructure upgrades instead of toward paying out dividends".
If anything, I would expect a publicly run utility to be less efficient at capital allocation. All "excess" capital may get used up in the inefficiencies instead of investments.
Consider the challenges of city-wide transportation networks in providing service, maintaining infrastructure and investing for the future.
Alternatively, neither private nor publicly run capital is good at discounting the far future.
Sending the capital to maintenance would be a politically driven project right now for public utility. For private company even right now it is still a conflict of interests between maintenance and shareholder interests.
Consider the following regarding NY, DC & SF subway systems:
"How Politics and Bad Decisions Starved New York’s Subways Disruptions and delays have roiled the system this year. But the crisis was long in the making, fueled by a litany of errors, a Times investigation shows." 2017 https://www.nytimes.com/2017/11/18/nyregion/new-york-subway-...
"Metro sank into crisis despite decades of warnings Metro’s failure-prone subway — once considered a transportation jewel — is mired in disrepair because the transit agency neglected to heed warnings that its aging equipment and poor safety culture would someday lead to chronic breakdowns and calamities." 2016 https://www.washingtonpost.com/local/trafficandcommuting/met...
"Past decisions haunt BART as it seeks voter OK for $3.5 billion bond" https://www.sfchronicle.com/bayarea/article/Why-BART-s-futur...
It's amazing we're debating the pros/cons of public vs private utilities while we have an example of an incredibly corrupt private utility that needs to be shutdown and with execs thrown in jail for gross negligence.