Property taxes aren't really an "Illinois" thing but a local government thing. Lake Barrington sends their kids to palaces 180 days a year, commensurate with their home lifestyles. I don't know Mt. Prospect well, but I had to scout some locations for an event in Wheeling Twp. 3 years ago and their park district facilities are better than the $100/month health care facilities. If your dad doesn't use such things, and presumably no longer has school-age kids, it may not be worth it to him. Of course, my mother stayed in O.P. long after her kids were done, and felt continuing to pay for schools was a responsibility to those who'd helped pay for ours.
50% or more of property taxes here go to schools in most IL communities, and a big chunk of the rest to the local municipality, with parks (though my parks are managed/paid by the muni), the county and various other small units making up the rest. For me, it works out to schools at about 70%, muni about 20%. The county, less responsive to any small set of voters and their concerns, is only about 7%. (And we're among the few that abolished our township govt. But I think township gov't ix <3% of the tax bill in most urban areas.)
The large differences you report in taxes for 3 similar sized properties in the same school district pretty much have to be because the properties have different values, since the county tax rate couldn't possibly have that big an effect. Price is a function of demand, which goes back to what I said above -- people prefer to live in these communities.
Basically, people in communities like Mt. Prospect get what they pay for, and most of what they pay for is the school system.
