I saw this week's episode being filmed and it was fantastic. Alexander Armstrong is as good as Angus as a host and Reginald D Hunter is always a brilliant guest.
I know that it's part of Paul's persona on the show to be deadpan and miserable and he's not at all like that when he's doing other stuff (like the comedy store players), but he was really cheerful and laughing at everything as well.
I've been a couple of times and the host does make a massive difference. A good host makes the show seem effortless, a poor host makes the show seem strung together and a little unnatural. I've seen Jo Brand, Alexander Armstrong and Al Murray hosting it; Alexander and Jo were brilliant. I thought Al Murray could have been good next time, but as his first time, he just let the show fall silent and left people with nothing to say for too long. Although, in fairness to him, the new stories that week were terrible, which didn't really help.
Like you say, they always need to have a vehicle for satire and that is the easiest way of doing it. HIGNFY is a lot cheaper than making a show with Rory Bremner or something like Drop the Dead Donkey.
HIGNFY has outlived all the other game shows and although it does have dips and highs in quality, it is for the main, very good. Nothing else comes close to it; I think that part of it's charm is that they don't just have the same circle of comedians who do everything, they also have journalists and politicians. You wouldn't see that on Mock the Week. And, as opposed to Mock the Week, the regulars let the guests talk!
I think that if either Paul or Ian decided to call it a day, that would be the end of the programme. Lets hope they keep going for a bit longer!

Afterall, I suspect it has given them a very good, steady income for 20 years and allowed them the time and money to do what they want.