Mode 7 on the BBC Micro is very different to the other seven display Modes (0-6).
From the programmer's point of view, the BBC Micro's mode 7 looks like 'oh, there is also a character cell mode that saves memory', but from the BBC's viewpoint it was also about supporting the existing Teletext standard. From the hardware engineer's viewpoint it may also have been about using the existing, proven and mass-produced SAA 5050 chip, which not only provided a high-quality character display, but also a hardware implementation of Teletext features.
It presumably also informed the color palette; according to a comment on the Stardot forums:
I thought Steve or Sophie had mentioned in one of their talks that the PAL encoder basically came from the BBC.
So reusing the existing color generator circuit designed for Teletext TV sets; that makes sense.
According to Wikipedia's article on the SAA5050 chip (used for Mode 7):
Full-screen resolution generated by the SAA5050 was 480×500 pixels, corresponding to 40×25 characters. Each character position therefore corresponded to a 12×20 pixel space. Internally each character shape was defined on a 5×9 pixel grid. This was then interpolated by smoothing diagonals to give a 10×18 pixel character, with a characteristically angular shape, surrounded to the top and to the left by two pixels of blank space. This gave a particularly stable and flicker-free arrangement on interlaced displays.
This also makes sense (well, except I'm not clear on how anything ever made interlace usable given how abominably it flickered when I tried it on the Amiga, but that's a separate question; I think the BBC Micro used progressive scan like other computers of the time).
While Mode 7 has an effective horizontal resolution of 480 pixles, the other modes have a horizontal resolution of 320 or 640. I would intuitively have expected 240 or 480 in a machine that incorporates the SAA 5050 as a core feature. Why choose 320/640 for the other modes?
Conjecture: By the time the BBC contract came into the picture, Acorn's engineers had already designed a bitmap video system based on 320/640 for the adequate and sufficient reason that this was the usual way of doing things. Given the very tight development schedule, it made more sense to accept a bit more manufacturing cost for two separate pixel clock circuits, than to redesign the bitmap video around the pixel clock for the 5050.
Alternative conjecture: Acorn wanted the micro to double as a business computer, for which an 80 column mode was highly desirable. The ideal would've been an 80 column character cell display, but in the absence of sufficient development time, they decided a 640-pixel bitmap mode would double as this while also having other uses.
Is either of those conjectures accurate, or is there another explanation?