FS?
I was a regular attendee at matches during this period, either at Anfield, Highbury
or Priestfield (Gillingham) as well as virtually every England match at Wembley.
Heysel and Hillsborough had a double whammy effect on most supporters, and the Government stepped up to seriously address hooliganism and crowd safety at sporting events. The concept of caging fans was obviously flawed as the cages were a danger in themselves. Those were the days of mounted policemen whacking anybody in sight with riot batons (I nearly copped a cracked skull at Villa Park after Man U fans rushed Arsenal supporters after an F.A. Cup semi final)
There is no real way of calculating the effect of the ban on hooliganism in a tangible manner, but there certainly was a sea change over those 4 or 5 years. The cages came down, seating was installed, clubs were required to employ ample well trained stewards. Fans saw their status changed from supporter to customer. Suddenly, you could wear your teams jersey to matches without fear of a beating.
It seemed that overnight, hooliganism reduced radically (although it was probably more like a season or two). It really was that quick.
Being a Liverpool supporter, those days after Heysel were very sobering. You also must remember that two weeks before Heysel was the Bradford City fire. At both Heysel and Bradford you saw the best and worst of football supporters. While some bravely risked their lives to save others, many more exhibited the mindless tribal outrage which is football hooliganism. (Which also occurred at Hillsborough)
Unless you have actually been in a situation with 10's of thousands of fans, it would seem hard to understand how decent supporters can react in that manner. I seem to recall Juventus fans throwing flares into the Liverpool fans. No doubt, before that, there was plenty of verbal abuse from both sides and possibly, pelting of bottles etc. I'm not blaming Juventus fans for the tragedy, but there is usually a spark that ignites an explosion. When it "kicks off" panic sets in, which often leads to pushing and fear of being crushed.
The implementation of proper segregation, organised policing and provision of emergency procedures all helped to reduce hooliganism as well as the restriction of alcohol sales and, of course, removal of standing on terraces.
Personally, I think the European ban didn't influence the hooligans, but it made the clubs, police and government address the issue as a matter of national importance, so in that way, the ban brought about change, but the changes didn't really gain pace until after Hillsborough, which really should have been avoided. Perhaps it took the death of British fans as opposed to Italians, for the authorities to really get serious?