the poor do not usually 'have debt', and when they do, the interest rate is high (payday lenders, credit cards). Inflation does not benefit people with high interest rates, it benefits people with very large pools of money borrowed at interest rates near or lower than inflation. That is mostly institutional investment and banks, and select high value leverage traders, a mostly wealthy subset.

The poor are hurt by inflation because their wages are more severely devalued by real value loss. If you're spending most of your wages on day to day expenses, the effect on "margin of survival" from a small devaluation is hugely magnified relative to if you're spending very few of your wages on day to day expenses. I suggest you work through some math on the back of an envelope to really understand this effect. An easy case: Let's say you are barely scraping by, spending nearly 98% of your wages on expenses and there's 3% inflation. What happens next? What happens if you spent 20% of your wages on expenses in the same scenario?

The common retort is that "wages catch up to inflation" but that's nonsense. The whole premise of inflation being used to stimulate jobs is that it devalues the real cost of employment: you can't have your cake and eat it too.

Finally, "encourage investment" well if you think that every investment is wise that is reasonable. However, inflation pushes people into investment. So what that effectively means is that cost of the risky business behavior of the top classes is socialized. You could also see it as 'encouraging consumption', which if you believe in conservation as a moral good, is antithetical.