Providing a CV won't make it any easier for you to get the job you're actually discussing. It just makes it easier for them to send you emails like: "I see you have 4 years experience with JavaScript. We have an exciting opportunity to join a team of rockstars working with Java and Spring".
There's another concern to be aware of: some unscrupulous recruiters will edit your CV. That is, if they see a job posting looking for someone with x years experience with Spring, they might just add that to your CV, even if you've never worked with a java stack.
For this reason I always carry copies with me to interviews.
About the CV thing I bet this is a legacy workflow that most companies still used to.
I dont even own word anymore.