It sounds good in theory but it could make for some boring bank holidays. If only staff working in essential public services could be at work, that would mean that (on, say, a rare sunny August Bank Holiday) a trip to the seaside would have to be without any ice creams, fun fair rides, meals in restaurants, drinks in pubs or shows in theatres. Indeed, unless public transport was designated as an essential public service, those without cars wouldn't even be able to go to the seaside.
Similarly, a day spent on DIY or gardening would have to be planned in advance, since it would be impossible to buy wallpaper paste or potting compost on the day.
The multiplier of 5.6, which you refer to, was chosen for a specific reason. Under the original rules, employees were entitled to 4 x the number of days they worked each week as their annual holiday entitlement. Some employers took that as excluding public holidays (or days in lieu of public holidays) and gave their employees (who worked 5 days per week) 28 days paid leave. Others took that as including such days, and only gave their employees only 20 days. In order to provide conformity, the rule was changed (in two stages) to 5.6 x the number of days worked each week (but with the stipulation that public holidays, or days in lieu, were included), thus ensuring that all '5 day' workers got 28 days holiday per year. The entitlement was also capped, so that people who work 6 days per week still only get 28 days statutory holiday entitlement.
Chris