you should care because often this agreement is not about the technical detail of cookies, but allowing the company you are interacting with to share data about you with 3rd parties.
If you think which HTML div element you click on to dismiss a sticky banner has any bearing whatsoever on how your data is handled server-side, I've got a trip to the Titanic in an Oceangate submersible to sell you.
Legally it does, at least if you're in the EU. The only reason websites are slow on the uptake around this is that the legal gears are slow, however we have seen many considerable fines in this space in the last few years and things are improving.