There's an interesting story here...
Up until a few years ago, there were no minimum TBN limits on either API PCMO or ACEA Conventional (ie not Low SAPS) PCMO.
Regarding API, although TBN has never been specified, there is an implicit 5 minimum TBN limit. This is what you typically need to pass the Ball Rust Test. This usually gets upped to around 8-ish with the extra 3 TBN being a highly cost-effective contribution to controlling oxidation in the early stages of the Sequence IIIF/IIIG test.
Regarding ACEA oils, you have to understand that stuff like A3/B3/B4 usually evolves as a secondary, not a primary oil spec. Ten years ago, if you picked up any can of oil in Europe, you would see it carried BOTH API & ACEA credentials (eg SL/CF/A3/B4). Indeed, the ACEA oil specs used to contain some US tests as well as European ones (don't ask me why, is just is!)
Anyway, because of this, in developing a Euro oil, you might typically start out developing a US oil (possibly with a boosted, more seal friendly DI). Once you had the relatively easy (primary) US tests in the bag, you might start in earnest on the (secondary) ACEA tests.
If you do things this way, you might expect to start your ACEA testing with an 8 TBN oil as it simply carries over from the US tests. As often as not, you could finish your ACEA program without upping the TBN.
However there was a 'political' problem with this. The whole Low SAPs thing kicked off in Europe with massive OEM support behind it, as they were all worried (with good reason as it turned out) about Diesel Particulate Filters ( DPFs) blocking. Low SAPs oils sort of evolved to be around 6 TBN. The powers that be in ACEA were concerned that (cheap) conventional PCMOs were 'too close' to the (expensive!) Low SAPs oils. As a result, the ACEA 2010 spec, for the first time ever imposed minimum TBN specs (8 min for A1/B1, A3/B3 & A5/B5 and 10 min on A3/B4). This overturned years of a guiding philosophy which insisted on oil performance being defined by engine tests and not by artificial chemical limits.
So there you have it. ACEA oils like A3/B4 will have a specified high TBN and you might think that automatically makes them better than than an API PCMO with no specified TBN. It does not...