Though around 25:38 the host asks about whether 1080p is becoming the norm for internet broadcasting - I thought it was. If it's a youtube program don't you want to shoot at 1080p (or higher) and have youtube automatically convert to all the lower formats (unless the reason is that they can't do that high a frame rate at the higher resolution or something)? Over the air broadcasts doing 1080i not 1080p - the BBC in the UK does 1080p (but only at 1080p25 not p50). But still, 1080i in the US is more pixels per sec than 1080p24 of Blu-ray and equal to the number of pixels per sec of 1080p30.
The host says "a lot of people say that 1080i is the equivalent of 720p29.97. I'm sure a lot of people don't say that - aren't they usually comparing 1080i and 720p59.94 - where they are very similar in pixels per second - and the argument for 720p59.94 would be that it compresses better. Though really the 1080i vs 720p is surely outdated (at least in terms of new formats). Also, the podcast is 29.97 fps when it could also be 59.94 fps. So 720p29.7 isn't equivalent to 1080i59.94 - in terms of resolution or temporal resolution - unless the 1080i show is shot/made in a progressive-style (progressive segmented frame) format (30 different pictures per sec), whereas 1080i59.94 can easily be approx 60 different images per sec (twice as much temporal resolution as 720p29.97 the host asked about). So you wouldn't end up with 30 frames per sec from 1080i - if it was a live show (eg. sports) - because you'd de-interlace to 60 frames per sec (even though it's stored 30 full frames per sec, you'd de-interlace to 60 because they're frame different points in time, and you don't want feathering+lowering of the output temporal resolution). So 720p59.94 doesn't have better temporal resolution (especially when it is converted from a 1080i59.94 signal in the first place) - except for the fact that it may be better able to handle more compression.
Also, surely an object in motion - eg. sports in 1080i60 (ignoring compression issues) isn't going to be any more blury than the same object captured in 720p60 - when output (when properly de-interlaced to 1080p60). If it's able to properly de-interlace it (to 1080p60), both formats will have the object blurred for 1/60th of a second (shutter open time). Though I suppose it depends on how good the de-interlacer is. If it's just line doubling the moving parts of the image, the object could be slightly lower res in height (fields) but higher res in width (1920 vs 720).
So I think the reason the sports channels went for 720p was to use a lower bandwidth without visible artefacting on fast motion - plus allow further re-compression further downstream without it introducing affecting pq too much. Other countries (such as the UK) use 1080i (when they're not transmitting "1080p25"), including for sport.