Powered main speakers and powered subwoofer? If so then you should be fine.
You could get in arguments about whether there is "better" and there always will be better. Many think it better for there to be some crossover to separate out the low frequencies, and send them to the sub, and send everything else, but not the low frequencies to the main speakers. As to a receiver, not all of them have separate subwoofer out connectors, and rely on the exact method you are discussing.
I don't think you will be disappointed with the setup as you are describing it. Not sure I have seen speakers with that much power in each one, mostly that describes the wattage capability of the speakers. Subs with 100+ watt amps built in yes, bookshelves? - I doubt it, but possible today with digital amps.
Then there is the argument against subwoofers in general, but that's a whole different religion.