E75, all your problems seem to be down to the handling agent of the airline you use.
Groundhog, you are almost certainly correct. Given some of the main airlines at BHX, and T2 in particular are also having to cut costs to the bone, you are probably right that this means the service level agreement from their contractors is the lowest possible cost, with consequences for staffing. Ditto Border Force, who are going to be well down the pecking order behind nurses etc...
That being said, to most passengers, most passengers would associate the ground staff with the airport (except maybe check-in & gate agents). And I do hear a lot of tutting and griping from fellow passengers as we wait to de-plane or enter the UK.
I think part of the issue with T2 is that I recall there was a plan to knock it down, back in the good old days (before Global Fiscal Armageddon), and replace it. So upgrades etc were neglected. Then once Armageddon actually happened, the business case disappeared in a puff of smoke, and the airlines using are either not interested in a good customer environment, or cannot afford it.