I'm afraid, I have to disagree with the premise. If it were indeed impossible to rein in ill-behaved employees as you claim, businesses worldwide would fail to function in a professional manner! And no minimum uniform and professional level of banking experience can be expected across different branches of the same bank, or indeed, at the same branch over time!
Even ignoring other countries, -- how was it achieved by Citibank India, for example, or, indeed, in some other Indian private banks as well (albeit to a lesser extent)?! How come Indian PSBs have managed to earn such widespread notoriety in this respect compared to their private counterparts?!
There must be various performance metrics in every business (even in the PSBs) linked to progress in the career path (increments, promotions, management ladder and so on). Why can't behavioral traits of employees be considered amongst such metrics, and appropriate demerit points be linked to eligibility for direct customer interactions, delay in career path progress, or even demotion or loss of job?!
I have personal experience with banks in India as well as abroad. Even amongst Indian PSBs, SBI seemed to have achieved this with their 'Specialized Persional Banking' (SPB) branches (do they exist anymore?). I was a very satisfied customer with one of them in Bangalore. How was it possible for SBI to achieve that? By assembling some of their "Great Bankers" in select branches (at the expense of lesser branches)?!
Still staying with SBI, I once had a BM so utterly arrogant and ill-behaved, I pulled out my very substantial investments with them (for more than a decade) to some other bank (to become one of their HNW customers). With the vaunted superior training system in the PSBs, how was this person even get to be promoted to be a BM? -- Of course, there was no mechanism for me to leave a formal feedback for my experience! Did this episode prove to be of any advantage to the bank? --- I have other examples too with other PSBs.
One of the root causes is that employees in PSBs (and other public sector units) are apparently secure in their belief that they can get away with anything, no matter what! -- Things are gradually changing, but not enough, nor fast enough. (Disclaimer: This is not to be construed as an endorsement of Indian private sector businesses, which have their own issues).