But most banks aren't the originator of that money. The Fed creates money, all other banks lend it out which causes a money multiplier effect. However, the money multiplier doesn't actually affect prices directly - beause most of that money are deposits, ie they're not being used. Money only leads to price inflation when its spent. Banks gain seigniorage by having first access to money lent out or spent by The Fed. If they need extra money to cover for too little deposits, The Fed is there to give those banks below-market-rate loans. If the government needs to borrow more money and banks don't have enough to buy the bonds, The Fed will buy bonds from banks at above market rates so those banks can buy more bonds with the money they get back from that. That's where the seigniorage happens.
There are also financial institutions that banks give benefits to (cheap loans for example). Those financial institutions also benefit from seigniorage by getting those cheap loans. Ordinary people aren't getting cheaper loans tho. If anything, the monetary inflation pushes loan rates up, even as nil resere requirements and a low discount rate have pushed them down.
If they spend it, poor people would still benefit because the spending is creating jobs in the process. Really, the only problem is land ownership (renting out buildings is fine) and that has nothing to do with inflation, rent seeking is a fundamental problem that drains productivity from the economy.
Sure, some rich people take out loans (but have to pay it back, which often they do by spending the loan on stuff that creates jobs) and some benefit very indirectly from asset prices rising. But as a general rule the poorest demographic borrows more than they own and lends absolutely nothing, and the richest demographic borrows less than it lends, and sees returns to its lending fall