Certainly any of the calculations may be performed using basic math, and the wind drift/speed can be done with trig and vectors.
But, for calculations, the big advantage to the whiz wheel is that it "automatically" divides (or multiplies) by 60, vastly simplifying the steps needed for time calculations (fuel burn, nm/hr, etc.)
The conversions (pounds per gallon, nm to km, etc.) are simpler, as well, rather than having a list of conversion factors, one simply lines up arrows and reads the answer. Then if you're talking about the usual flight computer, those small windows used for true altitude, true airspeed, and density altitude are way easier than consulting tables of numbers (though, the tiny coarse number scales make it unrealistic to get very precise numbers). Remember, also, part of the elegant simplicity of the E6B is it's ease of use one-handed while flying in perhaps turbulent air. All that said, in reality, once through the exams as a licensed pilot, your trip calculations, as well as weight and balance, are most likely to be accomplished using one of the many excellent flight planning apps available for tablets or smartphones. But, personally I think use of those apps, or the dedicated electronic E6B calculators, at the student level of flight planning, may leave the student with a lack of understanding the fundamentals of a given problem, even though they may turn out a "correct" answer. IMHO, as a long-time instructor, my recommendation would be, at least through your training, to keep at the old-fashioned whiz wheel till it's easy for you to use.