What's the point of adding security features to new bill designs? What's the point of creating new bills with more security measures to prevent counterfeiting? (For example in the USA the new $100 bills have more security features).

If the old bills are still acceptable as currency, why would anyone even try to counterfeit new banknotes with all these security features?

Why don't people counterfeit bills from the 1800s (which are still legal tender - USA) and have NO protection from counterfeiting at all?
Bills don't last that long. The Federal Reserve estimates that $100 bills last about 15 years. Therefore, old bills are fairly rapidly rendered quite rare. Bills that look really odd (like the rare ones) are likely to warrant a second glance from the acceptor and later, if the counterfeiting is uncovered, much more likely to be traceable back to the forger. In The Great Paper Caper, Wells Tower tells the story of Frank Bourassa a counterfeiter who focused exclusively on modern \$20 bills because the enormous scrutiny on \$100 bills in general.