It's not the rule in the U.S. that deposits must be in dollars. (Most banks will let you open up foreign-currency accounts...they just charge more. A lot more.)
However, foreign currency-denominated accounts are subject to yearly gain/loss recognition as the value of the foreign currency changes compared to the dollar. This could potentially trigger income taxes on the unrealized gain, effectively (and usually) reducing or eliminating any interest earned. It's also a PITA for banks to deal with the compliance paperwork.