It's not quite universal to say inflation robs from the poor. Some poor people like your fixed-income grandma example are hit hard by inflation. Some are hardly affected since they live paycheck to paycheck and don't keep savings. Others benefit from it -- in particular, those who have more debt than savings. Inflation is good for debtors and bad for creditors.
Anyway, I'm hardly opposed to keeping inflation low. I would be fine with 0 inflation, for that matter.
By 0 inflation, I don't mean a fixed money supply. I mean $X pays for about the same amount of goods 10 years from now as it does today.
Accepting limitless deflation via a fixed monetary supply is just as absurd as accepting limitless inflation.
It does not make sense to base a monetary system on a token that represents "1/k of all the wealth", where k is a constant. So just by stuffing the token under your mattress, contributing to zero economic activity, you reap the rewards of all economic growth that added wealth to the world.
Here's how I see it:
The US M2 money supply grew from $286B in 1959 to $19,670B in 2021.
With that came inflation: a dollar in 1959 could buy roughly what $9.13 buys today, according to the BLS.
But that level of inflation is not even close to 1:1 with the money supply increase.
The money supply grew to almost 69x its 1959 size, but the dollar is worth 1/9th what it used to be, not 1/69th. That's because the whole pile of dollars put together are representing more real world wealth than existed back then. The economy has grown, more people are participating in it, and it's making more stuff people value.
Maybe the correct level of growth in the money supply would've been 9x smaller, for no inflation. So the dollar today would buy roughly what it did back in 1959. I suppose that would be OK. But that's still a money supply increase from $286B to $2,193B.
What if the money supply was fixed? So instead of roughly 9.1x inflation, we'd have roughly 7.7x deflation: the dollar today would buy 7.7x the stuff it bought back in 1959. How is that fair? Grandpa's pay for a day's work back in '59, which he put in a safe and forgot about, is worth what I get for a week and a half of work in 2021? Talk about oppressing the poor, you're never going to beat "old money" in this system. The longer the family has been wealthy the more unattainable their savings will be in terms of present-day wages and earnings.
And that's all assuming the best case scenario, which is that the 7.7x economic growth still happens with this deflationary currency. I could easily see it being lower given that there's less incentive for anybody to invest in businesses.