Is an American waterfall (distribution) ever preferable to a European waterfall for an LP?

Waterfalls outline how cashflow will be distributed between general partners and limited partners. In the European version, the GP (sponsors) do not receive carry until the LPs original investment is returned and preferred rate of return is met. In an American Waterfall, however, carry is distributed to the GP before the LPs’ funds are fully returned.

Would an LP ever favor an American Waterfall over a European Waterfall? Would an American Waterfall ever confer benefit to an LP a European Waterfall would not?