Do subwoofers really help?

I'm not crazy because when I replace my speakers with less sensitive ones (Focals for example) 2 things happen...Bass improves, and I don't have to turn the volume up as high to get good sound. I am an amateur and I did not pay attention to the specs on the speaker before purchasing. The Imepedance curve on the speaker is too steep. I am not buying a $4000 amp just to drive them.

Thanks everyone I found a solution.

I actually took everybody's advice. The problem was the impedance curve on the speakers was too steep for the amp, but I liked the amp better. So, I sold the speakers and Got ones that better match the amp. The peak output on my amp is 4R. The impedance on my new speakers never drops below 4R so there are no issues. I can tell this was better than adding a sub because now I do not have to turn the dial on the amp as high to play them loud. Sorry for not being more specific I am sure I am not the only person to have done this.

I spent no extra $$ to do this I got good $$ for the speakers I had.