I'm from EU, I had the time to look at the recent amendments about this law, in which they added precisions about the fair use of data, for non-profit and public research.
They also precised that this law and the technical implementations should not go against already in-place freedom of speech rights.
Hopefully, people will be able to easily defend themselves versus the big corporations in case of abusing take-down requests. The recent example of Twitch streamer Lirik being unrightfully suspended on a simple request from UEFA shows there will be an adjustment period for everyone involved. His case was quickly resolved and he was unsuspended in less than 24 hours after the take down request. However, he is one of the most famous streamer from the Twitch platform, he can easily use his social network to acquire visibility. For smaller and not well-known streamers, it may be more difficult to obtain justice...