Social mobility - is it 'replace-the-toffs'? Or, 'move-into-the-gaps'?

A few queries about 'social mobility'.
This is bandied around like its a necessary social good. I'm always suspicious when the Right talk about something that seems egalitarian as if it's good as they spend a lot of time berating the Left for being egalitarian. So, the social mobility they're talking about must be within the status quo, presumably. Assuming a fairly constant population, then 'social mobility' must mean 'less advantaged people' (as they would put it) moving upwards socially to replace usually more advantaged people. Again, presumably, they mean they do this by virtue of their ability thereby replacing those in that position not by virtue of their ability.


Grammar schools - like the one Theresa May went to and which, she believes enabled her to compete with the toffs - need to come back so that people like her (she believes) can properly compete with the toffs again, and, presumably, replace toffs at the top.

However, the social mobility that people talk about in relation to the grammar schools of my era (1944-1970) are usually talking about 'bright' working class boys and girls who moved upwards into administration and professional jobs where before people of that background hardly figured. This social mobility hardly involved replacement (along the lines I described in previous paragraphs). What happened were two things: the administrative and professional layers and experienced some losses due to two World Wars, and - even more importantly, this was an expanding economy. In other words, there were gaps that needed filling.

So in the here and now, which is the social mobility they're offering: 'replace the toffs'? or 'move into the gaps'? Or both?

And where is the evidence that either of these processes needs segregation at 11 to achieve that?