I think you have a different definition of "different lines".
BART is like a tree. The branches join together into one trunk. It's shared tracks into the same stations. So measuring the frequency of all the lines makes sense, as long as you only want to move between stations on the trunk.
London is not like that (if I understand correctly). Elizabeth and Thameslink don't share tracks between common stations.
So London has much higher aggregate than BART. But the statement about BART's train frequency on the trunk is not a nonsense statement.
Another analogy might be the NYC subway, where in Manhattan you have lines like 1/2/3, A/C/E, B/D/F/M, N/R/W etc. that share a number of stops in southern Manhattan, so along the 1/2/3 or A/C/E, the sum of tph matters... but as they break from that "trunk" in the boroughs, or at the ends of Manhattan, the individual lines matters.
Some of London's Underground lines do share track along some of their length, like BART, but overall this is an exception rather than a rule, e.g. some of the District and Circle overlap, and indeed the Metropolitan also shares with the Circle.
And I agree that for the purpose of a trip within this core, you'd only care about that 5 minute wait, which is pretty reasonable, much as often passengers won't care if this is a District Line train or a Circle, since the stop they're going to is served by both.
OK, so it's about 12tph on bart on the core stations? Disappointingly difficult to get a map of bart which wasn't geographic.
So all the lines share track from Daly City to West Oakland, with some extending to Millbrae, and then branches on the east side of the bay?
From the map, it looks similar to the Picadilly Line, or Central line, or as mentioned upthread the Metropolitan line, but BART has 12tph on the core, where those services have twice that. Each "line" is just a branch on a core service.
The longest run is 53 miles (there's a completely separate service), which is a bit more than the Picadilly line (46) but not massively, and the frequency is under half that of the Picadilly. I think it's fair to compare BART with a single London Underground line (like the Picadilly, or the Central), just with half the frequency.
BART is like a tree. The branches join together into one trunk. It's shared tracks into the same stations. So measuring the frequency of all the lines makes sense, as long as you only want to move between stations on the trunk.
London is not like that (if I understand correctly). Elizabeth and Thameslink don't share tracks between common stations.
So London has much higher aggregate than BART. But the statement about BART's train frequency on the trunk is not a nonsense statement.