This is common practice in mountain biking. Before I sold my trail bike I was running 2.4" front and 2.25" rear. Mainly because I couldn't fit a 2.4 in the rear stays.

The bigger tire in front also had larger knobbies. So traction on loose over hard and mud was incredible. And then I would run a xc style low profile knob tire in the rear to decrease rolling resistance.

The only reason you'd ever need a wider rear tire is for loose surface traction when hauling a__ or climbing really steep stuff. Because physics, the rear wants to track wherever the front is taking it so it's gonna get you there even if it's narrower and more slick than the front.