Yeah, I've seen a lot of "well, III happened in 1994, so who's going to remember that?" comments. But III was so
bad, it's hard to forget about it, and like it or not, III was the last Beverly Hills Cop film. Plus, as you said, III was the start of Murphy's long and painful barrage of shit films, and III has been panned to death over the years as one the most infamous turkeys in Murphy's career. Another thing that pisses me off about III is, they killed off the one guy (Todd), who still had some spunk from the first two films in the beginning.
So yeah, III was so god awful it's going to be damn near impossible to come up with something that'll be a better film. I'm 99% sure 4 will just be a cash-grab sequel for Hollywood to cash-in on the nostalgia from die hard fans of the franchise. You know they're desperate for new ideas, when they announce a remake for The Butterfly Effect Setting (seriously, the original with Kutcher is only like eight or nine years old). Setting the bar low for expectations, but hopefully they won't tweak or tamper with this classic theme too much.