Score indications of pedaling are not really set in stone. A performer will adjust pedaling to suit the instrument and acoustic. One of the exceptions is when a composer wants a specific special effect with the pedal, but that is not the case here. The pedaling indicated in your edition gives emphasis on the 1st beat in the bar, which brings out the waltz character of the piece. If you are finding beats 2 and 3 too dry on your piano with these markings, you can try fractional pedaling: that is don't push the damper pedal all the way down, only depress part way. Full pedal on beat 1, fractional pedal on beats 2 and 3. Use your ears to guide you.