> What it does is increase borrowing.
But only in the short term, since lenders will catch on and increase their interest rates to offset the inflation. As you said, you're transferring wealth from lenders to borrowers, which means a larger incentive will be needed to induce anyone (other than the Fed) to lend money. To maintain the effect you would not only need to maintain the inflation but also continually increase the rate of inflation to exceed expectations. That's a quick route to hyperinflation and worthless currency.
The Fed can keep lending at arbitrarily low rates long after every other lender has been driven from the market because they're "lending" newly minted currency at essentially zero cost, and moreover don't particularly care whether they make a profit. However, even they can't sustain ever-increasing rates of inflation without destroying all confidence in their own currency, and it's pretty hard on the other lenders. ("Lenders" including anyone with a savings account, or with a significant fraction of their net worth in currency rather than inflation-proof assets and other investments; the poor are thus hit harder than the rich.)
> ... the people who want to build new factories need money to do it ...
That's an over-simplification. The people who want to build new factories need materials and labor to do it, not money. Giving them more money doesn't increase the amount of material or labor available, though it may allow them to claim a larger share of the available goods provided they do so before the inflation becomes generally known and devaluation takes effect. Naturally, if they're getting a larger share then others are making do with less. It only works out to a net benefit under the assumption that you know how those goods should be put to work better than the people directly involved—despite apparently being unable to persuade people that your plan is better rather than resorting to underhanded tricks.