Also while The Day Today was styled similarly to the evening news programmes in some senses, the segmented format with separate sport and business desks as well as extended promos and genutainment segments were't really seen in either the News at Ten or the Nine O'Clock News at the time and is a closer format to Breakfast programmes, like the Channel Four Daily.
True, but it was also something that at that time CNN were doing. It's well known that in CNN's early days, their definition of 'news' was 'loose' to put it mildly, including things like business, sport, weather, showbiz, style, recipes and even fitness routines. It's as likely if not more so, that CNN was in part being parodied by that, rather than the Channel 4 Daily, which by 1992 had long since lost Comic Book, Countdown Masters and Streetwise, and was nothing more than News, Business, Sports, Weather and Arts news.
You also suggest that Daily can't have influenced The Day Today as it had finished before the latter aired - yet the programme must have been mainly, if not entirely produced in 1993 just months after Daily finished.
Yes, months after the Daily had finished but about 2 years after the original format, the one you are referencing was dumped in favour of a more serious format that removed elements like Comic Book and Countdown Masters from the mix. The difference between the original format and the later format was like night and day
While nobody is saying it was the only influence, it seems that the format of The Day Today was influenced by programmes like Channel 4 Daily more than anything else. Either that or it is a massive coincidence.
I think you'll find CNN was more influential in format terms than the Channel 4 Daily was.