Interesting point. While I see what you're getting at, a lot of times it comes down to the specific product available and I'm not certain I like any of the other 5w40 LL04 options much better; (look at the VOA for the Red Line Euro Spec 5w-40, below.)
If I were to go to a LL-04 in 5w-40, I'd probably lean towards the Red Line Euro 5w-40 but I wish they would tell me more about their flash point (not terribly concerned because I know they use a full synthetic ester base stock formula, and their pour point is indicative of a good base stock,) but I'm not sure what their sulfated ash content is, (assume it is around .7~.8 whereas my Ravenol VST 5w40 has a 1.05.) While Red Line's Noack of 6 is better than even my Ravenol VST of 7.4, it does also have a higher HTHS of 4.3 compared to 3.8.
I don't know, will have to consider the Red Line Euro 5w-40 LL-04 the next time around, even though I do really like the Ravenol VST 5w40 product based off a PAO with USVO. I think Red Line's ester base stocks are pretty good, as well, though. I do run about 4oz of Red Line's SI-1 Complete Fuel System Cleaner at every fill, usually Costco 93 with 5x the detergents as required by the EPA to be classified as a Top Tier fuel.
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LL-01 (2001). API SJ. ACEA A3/B3. SAE 0W30, 5W30, 5W40, 10W60. The first revision with detergents and additives brought in to work with the ridiculous 15,000 mile oil change interval that BMW promoted at the time. At the same time, certain components of the formula were removed or reduced (ZDDP). However, once cars and engines were out of warranty and mileage accumulated the nasty effects of extended oil changes were realized (i.e. oil sludge). LL-01 is compatible with engines approved for LL-98.
In 2016 BMW announced new 0W30 to replace 5W30. 0W30 carries the same LL-01 approval with a FE label, making it backwards compatible but also making newer models more fuel efficient.
LL-04 (2005). API SN. ACEA C3 (similar to A3). SAE 5W30, 5W40. The LL-04 oils have been greatly misunderstood in the past but this is now in greater demand. Most LL-04 oils are intended for Diesels, although it was also approved for gas engines in Europe and other world markets. BMW never certified LL-04 for the US (see next paragraph). Diesel oil has long been valued by engine builders and tuners because of its higher levels of ZDDP and higher HTHS ratings, both are excellent indicators of engine protection at higher temperatures. LL-04 also has a lower SAPS value which is good news for direct-injection engines (all BMW turbo engines since 2007). You won't find Genuine BMW LL-04 sold here but Red Line Euro-Series oil is produced around this standard.
As part of the efforts to make engine oil more environmentally friendly, the US EPA required ZDDP levels to be reduced in gasoline oil. However, Diesel oil was exempt from this ZDDP reduction. BMW never certified LL-04 for the US market because a) there weren't many Diesels for sale here, b) it was incompatible with the high amounts of sulfur and Ethanol in US fuel. However, since 2014 our gasoline more closely matches European formulas and interest in LL-04 has increased. LL-04 and LL-01 are interchangeable/compatible but LL-04 is preferred for its higher ZDDP and low SAPS.
https://www.bimmerworld.com/BMW-Engine-Oil/
https://www.youtube.com/watch?v=yjNxfOoouso
https://www.bimmerworld.com/Red-Line-Euro-5W40-Engine-Oil-Quart.html
https://www.bobistheoilguy.com/forums/ubbthreads.php/topics/3877347/RedLine_5w40_Euro