The -ess ending has historically been known to have been used in an insulting way, such as calling 19th century female poets “poetesses”. Not every person who used this term meant to insult women, but some did so it’s to be expected that people would want to move away from a potentially insulting form of referring to people.
I've been under the impression that in Israel today, people often tend to drop the possessive suffixes (as in דודתה) in favour of using the less formal של, so in this case most people would tend to say דודה שלי. Am I right, or do people still routinely use the possessive suffixes in everyday speech?
The only one that EVERYONE uses is אחות. Some other family members and plural books and a few other things are used by some people and they aren't made fun of. (If you say, אני פותח את חנותי, you'll never be able to live it down unless you live in a community of authors and public speakers.) The word אחי is used in slang as "bro", but even that, they also say "אח שלי" a lot for the same use. (Btw, even the word אחיות isn't used in one word possesively. It's EXCLUSIVELY אחות)