The only way I knew there was a train in Section was because I answered the Bells and used my Block Instrument. If the Crossing Keeper does not have a repeater instrument then the only way he is going to know there is a train in section will be by phoning the controlling Box.
In this situation the crossing keeper would have a repeater instrument (or some equivalent technology that gives the same information - even a CCTV camera looking at your instrument would work*) meaning that, yes, they will have the same information as the signaller. Your initial assertion was that there would be no way for a crossing keeper to know the location of trains. I replied that they would have at least the same information as the signaller - which you rejected as impossible before giving an example of how it would be possible.
I'm not saying that giving the crossing keeper this information would be sufficiently cheap and sufficiently useful that it would make employing one worthwhile in every situation. Obviously it would not. However, it is likely that in some locations it will be both affordable and sufficiently useful, therefore it is wrong for you dismiss the idea out of hand.
A Crossing Keeper is a Grade 1 Signaller, therefore he will be employed by Network Rail, and will be nothing to do with any TOC.
My comment was about funding, not about who employs them. It is perfectly possible for a TOC or other organisation to pay Network Rail to employ one or more crossing keepers at a given location, should they choose to do it. I'm not saying they should, I'm merely saying they could.
I see no relevance to your last sentence.
It was an analogy aimed at getting you to understand the fallacy underpinning your argument:
Saying that it is electric trains in the Thames Valley would not be an improvement over diesel trains in the Thames Valley because it is impossible to run them on the West Highland Line is obviously incorrect.
Saying that it is impossible to improve the status quo at any level crossing because one suggestion for how to improve the status quo would be impossible at one location is equally incorrect. Especially when it it turns out not to be impossible.
*Obviously there would need to be safeguards, such as if the instruments are not visible or unclear for any reason then the crossing keeper is to assume there is a train in section.