There's one more example I can recall, which I've posted about before. Surprise Surprise from the mid-nineties included BT sponsorship logos during the titles, with phone calls/connections the whole theme of the titles. The only video I can find is here
A simple bumper around the programme is obviously much easier. Don't need to worry about new titles when you change sponsor, or repeats of your DIY show end up on some obscure digital channel at a later date.
The Chart Show had the sponsorship logos integrated into the titles too. In fact the 1994-96 titles have Twix logos everywhere, to the point you probably wouldn't be able to cut them out if those episodes had ever been repeated.
The first series of the 90s version of Play Your Cards right had the News Of The World sponsorship integrated too, which is why the titles seem to begin to abruptly when Challenge repeat that series.
One series of GamesMaster had the McDonald's M morphing into the GamesMaster M as well. I beleive that was the series Dominic Diamond didn't present, due to not agreeing with McDonald's sponsoring.