Why progressive taxation is better than 'People's Quantitative Easing'

Jeremy Corbyn and John McDonnell and their economic guru Richard Murphy have spoken frequently of their plan to use quantitative easing (increasing the supply of money in the economy) to help fund projects such as housing construction, green energy production, digital infrastructure etc, as a way of creating jobs, getting the economy moving and solving some of the social and environmental problems that we currently face.
While I agree that these are laudible aims, I am not sure that quantitative easing (QE) is the best way for a future Labour government to go about raising revenue.  My reason for this is as follows:
Any increase in the supply of money inevitably decreases the value of money that people already hold, and this affects everyone in equal proportion, eg. a 2% increase in the supply of money means that, all things being equal, the value of all previously existing money decreases by exactly 2%.  In other words, QE operates as if it were a flat tax on everyone, including the low paid and those on benefits.  And since those with low incomes spend a higher proportion of their earnings on essential goods, they are more detrimentally affected by a decrease in the value of their money than those who have more of the stuff. QE, therefore, like VAT, is effectively a form of regressive taxation.
There is an argument, which may well be correct, that as long as there is excess capacity in the economy then increasing the money supply to fund investment should not cause inflation - the increase in available goods and services should counteract it (because the more products that are vying to be bought by those that have money, the greater the demand for money, thus increasing the value of money relative to those products).  However, even if this is the case, it means that, to the extent that the increase in goods and services were to be funded by some other method  - one which did not impact on the low paid - those at the lower end of the economic scale would benefit from an increase in purchasing power, which QE denies them.
For these reasons, I think that a better way to fund necessary and beneficial infrastructure projects would be to use some form of progressive taxation - rather than QE which, as explained above, is effectively a flat tax - so that the real cost of investment is distributed in a way that does not impact disproportionately on the low paid.