I think when an airline use minimum crew on a flight, the cabin crew are there for CAA safety regs. only (door coverage etc) and therefore do not have to complete a full service (if any!). Pax are probably unaware of this and it's actually very cheeky of LH to reduce service costs in such a sly way.
BA wanted to reduce crewing on certain shorthaul routes to the extent that an A319 would have 3 crew only and a B757 only 4, even if full. This so far has not gone ahead as the unions feel the pax's safety and service standards would be compromised for the sake of Rod's BEP!
A lot of the time, the crews don't do certain things because management tell them not to! I always remember a crew circular at BA a few years ago, when I worked there, that basically told crew not to 'show' champagne on the trollet top as pax were more likely to have it!!! Passenger first???