Fresh eggs are harder to peel when hardboiled, because the whites haven't started shrinking away from the shell yet. I find it isn't as big of a problem if you shock the eggs during the cooking process - cold eggs into boiling water, and then cooled down rapidly afterwards. I also notice fresh eggs don't blend as well when scrambling/mixing as well, though I don't usually find it noticeable enough to cause issues (if you're making something like a silky smooth custard, it could be an issue).
You can let the eggs sit a little (my eggs are usually around 2 weeks old by the time I eat them) - they'll still be plenty fresh but should be easier to work with.