Florida has no income tax. It has a higher sales tax to compensate (and other tourist-related taxes, such as on hotels and rental cars). Our property taxes are very, very low compared to other states though.
You're correct in that you receive an exemption if the property is your primary residence, but you overstate the burden of property taxes on >$1MM residences (its really not that high).
People purchase a high dollar value home in Florida because there is no limit to the value protected from creditors (except notes tied to the house) in the event you're sued or declare bankruptcy (1/2 acre of land or less within a municipality, 160 acres if you're in an unincorporated area).
Source: I'm a Florida resident.