Except the services that TfL control are not national railway. They are local urban and suburban services almost entirely within the area in which the mayor is accountable - exactly the same as the London Underground and DLR. Exactly the same way that there is local government and/or PTE involvement in local services around Leeds, Liverpool, Glasgow, Newcastle, etc.
From the perspective of a passenger, the improvements to the service brought about by this local involvement in local services is unquestionably a Good Thing.
Now if TfL were running an intercity franchise (something they explicitly have no interest in doing) then your arguments might carry some weight, but as they are it just feels like objecting tohe concept because you don't like the name.
How many national rail services in London run on completely self-contained tracks? In other words, they don't in any way interact with rail services which run outside the London area.
The only examples which readily spring to mind are the North London Line and Barking-Gospel Oak, and that's only if we exclude freight.
We have a silly split on the West Anglia side, with half of the inner-suburban service being run by LO, but the rest not. Inefficient use of trains and inefficient use of crews, and the LO part doesn't feel accountable to those who use it from outside the London area.
If we take something like the Great Northern inner suburban services, a route Mike Brown and his cronies have been said to have in their sights, virtually every service terminates well outside London. This is simply not democratically accountable, either to users of the services concerned, or for other users who share the same lines - and whose areas aren't already well served by other forms of public transport like LU or buses.
As someone who lives outside London, I don't wish to be involved with things like Sadiq Khan's re-election gimmick policy of the fares freeze. It's already damaging LU, and we don't need such politics on national rail too.
