This is one of the few things you view can view wholeheartedly through a political lens.
Mayor Khan has almost if not total control over the issue.
He holds the purse strings when it comes to non-routine cleaning, if lack of money is the reason tagged trains are being seen in service more often. He has the sole authority to direct TfL to take a tagged train out of service even if that leaves a gap in service, if that's the reason they're seemingly a more common sight. He even has the final say on livery and application, if there is a change to be had that might make it harder to tag a train and easier to clean it when it happens.
If the issue is a rise in the sheer flagrant disregard for the law by miscreants on station platforms, he has by far the greatest power of any local politician in the UK or even any Mayor in the (free) world, to direct and even fund specific policing to prevent/detect this crime. He even has ear of the Prime Minister, who seems to have no qualms about fast tracking the wheels of justice to send young offenders to prison to send a message. To say to the country that vandalizing a tube train, a crime that strikes at the heart of civil society and carries huge expense for the working people of London, is unacceptable.
Although not remotely comparable in terms of the severity and impact, I see parallels with London's failure to get to grips with knife crime, and what blame for that can be apportioned to Khan. Offenders form a small (tiny?) proportion of their socoio-economic demographic. It's a circle and activity that easily lends itself well to intelligence led policing and community based prevention. Preventing young people seeing this as cool, or at a minimum making sure the consequences outweigh the benefits to those seeking to be cool, is a far more effective and far cheaper (in the long run) approach.
In extremis, swift, public, and harsh justice, would have a powerful effect in terms of preventing and deterring, and might even lead to a whole host of other benefits, since it seems unlikely that these offenders aren't a burden to society in other ways. If you don't see tagging as wrong, or see it as an act of rebellion, what else are you up to?
And of course, offenders might not even be bad people doing things because they're bad. They might simply be people failed by society. A lack of opportunity, social mobility, a sense of exclusion, if not literally excluded. Nothing to do and nowhere to do it. No hope. That's easily fixed by someone with political influence and literal powers the Mayor of London can wield.
The Mayor is the custodian of the image of London. As well as being Londoner's literal custodian.