No disrespect to the places you list LAX, but they are hardly busy and can probably cope with the extra a little easier. Everything about MAN is at stretching point.
And with respect back, I don't see how that should affect things. Surely the staffing levels would be to the same ratio to traffic.
For example, PIK only has a few Ryanair flights per day, so, you would assume the staffing levels will be matched to the level of flights. Yet they accept diverts fairly willingly.
BHX has a similar airline and handling agent portfolio to MAN, albeit on a smaller scale, so, one would expect the staffing levels to be on a similar scale to Manchester, but just based on the levels of their traffic. They accept diverts en-masse.
LPL primarily handles low cost traffic. Low cost airlines notoriously pay less for handling etc. therefore, you would expect LPL staffing to be 'tight' to match its low cost mantra. They accept diverts en masses when they can.
NCL, GLA, EDI and so on.
The point is, they obviously have a decent staff > flight schedule ratio that allows diverts to be accepted.
The fact MAN slaps on the no div notam at the drop of a hat, primarily due to staffing levels, means their staff > flight schedule ratio is poor. And one wonders how it got in that situation when other airports seemingly cope well.
It's not about the size, it's what you do with it that counts.