It's a personal thing, but I feel mildly uncomfortable with leaving an APU on all the time on an ETOPs flight. We've been doing transatlantics with 737s, so a roundtrip will have the thing running for about 13 hours continuously. I think it's a safety thing- a jet engine with attached gearboxes driving compressors and generator constant speed drives all buried within a fuselage..... obviously Boeing are totally happy with it though. There has been a history- remember the BAC 1-11 (was it Frontier?) that had the tail burn off inflight back in about 1967 because of APU uncontained fire or exhaust leak. I have started a 737NG APU first time at 41,000', so for the very remote possibility of engine/generator failure, I think it is an unnecessary precaution.
But as for running it in the air in normal ops- there is absolutely no point. You have time to get it started if needed. Only if you despatch with a generator out is there any excuse.