From my observations (note, I don't drink alcohol on a flight so I have never been told personally that they did not have what I asked for, except for the Royal Blue Tea in JL F, but that is tea, and not available on BA!) that the booze availability tends to be bit of an issue on more 'leisure' focused routes (esp. champagne), not the cabin crew workload.

I haven't seem them running out of all forms of booze but have seen them run out of champagne - not surprising as some people were knocking them back very rapidly though! I can't remember ever seeing that on a more business-focused route, but TFS would be a rather leisure-focused one of course, so you might find they run out of champagne about half way through the flight.

I fail to understand the attraction of champagne in flight to be honest. Is it people's usual choice of drink, or do they mainly drink it in flight but not elsewhere?