No? Privately owned utilities with guaranteed return rates will charge more to guarantee those return rates. A publicly owned utility would be fine operating at 0% returns.
A public utility has little incentive to be efficient as like you said, they are fine with 0% returns.
If a private utility gets a rate of $1.00 on $0.94 of expenses, it has an incentive to further reduce costs to increase the return, which reduces future rate growth (as higher rates won’t be approved).
Studies show the opposite is true. Nobody gets voted out of the municipal rate board for denying rate approvals and allowing maintenance and capital investment to fall by the wayside. It's one reason U.S. infrastructure is in such terrible shape.
CPUC members in California aren’t voted in, they are nominated by the Governor.
So CA is a unique situation where the regulator effectively controls the public utility so calling it “private” is a bit of a stretch. More like a state controlled entity that trades on the stock market.
If you’re talking about California utilities the rate decisions are all on the CPUC website.
Rate increases absolutely aren’t rubber stamped, the CPUC routinely denies expenditures and the comedians rate increases.
But speaking more of the hypothetical, if set up correctly a regulated private utility could be incentivized to reduce costs to capture a higher profit at the same rate.
Investor owned utilities have more access to capital. The credit union / non-profit / co-op / municipal alternative is not an automatic win for customers.