Also inflation in the range of 1%-3% is considered a good thing because it helps encourage trade and prevents deflation. The amount of interest one can earn in a savings account or CD should also be taken into account.
The money weren’t distributed proportionally to the wealth of the people. Another reason, which though applies only in short- and mid-term, there are various nominal rigidities: contracts mostly use nominal values.
> The second question is whether inflation if it does occur is net bad/good and for who.
Well, that’s a whole nother question. You can create inflation using direct deposits to the holders of money.
If we're doing child-like examples, if the central bank prints a trillion dollars in notes and then sends them to the moon and promises never to use them, is anyone really poorer?