I can understand and appreciate the drives to keep costs down, and to try to future-proof. As an A.V. systems designer and installer myself then it's something I come across frequently with clients. Here's my thoughts based on seeing through projects from design to completion and servicing them once the clients have lived with them a few years. Please bear in mind that you haven't told us your family circumstances, so, some of these points might not relate directly to you if you haven't got kids in the house.
Future-proofing today for anything further than 3-5 years is a bit of an impossibility. Tech moves too fast. What you can do though is make it easier to adapt to new technologies as and when they arrive.
What I advise my clients planning a new build or major refurbishment is don't try to flood the place with cables today just in case. Chances are you won't use them before they become redundant. Instead, put in pipework with a big enough diameter that will make it easy to run new cables in the future. Where you need to turn a corner, either put in two 45 degree bends rather than a 90 degree - it will make pulling cable easier. That, or fit an access cover at the 90 degree point. Put in draw strings too. Sometimes you'll be pulling out an old cable to replace with something of a later spec, in which case the old cable can be used as a pull cord. Other times though you'll be adding a new one, so cover both options.
Kids above junior school age don't watch much linear TV, so the idea that they'll want to watch the same channel as on the main TV, or watch the same movie but in their own room rarely reflects reality. The go-to services that kids gravitate towards are online streaming. YouTube vids - yes, Netflix/Amazon Prime/Disney+ - maybe. Linear TV doesn't figure highly unless it's a program that is trending and that can't be seen via catch-up. Hardware of choice is the phone, the tablet and the games console.
Portable devices usually rely on good wireless, so cable up for WAPs in strategic points in the house. Other stuff such as consoles and smart TVs can go hardwired. The more stuff you can get off the wireless network then the better the wireless service will be for those devices where it is the only option. Put network cable points behind where TVs will live and behind where consoles will live. Don't waste your money putting a network point in the corner of the room. No-one wants to run Ethernet cable around the edge of a room and snake it up the wall to the telly. Waste of cash, even if your spark suggests it, just say no.
Ditto above for the idea that your kids will watch the same film as you in tandem but in their own room. If everyone is going to watch the same film, then watch it as a family.
Make the lounge/TV viewing area the place to be for family viewing. Good TV, great sound, lots of comfy seating, good lighting. There are other solutions to making your film collection accessible around the house. Rip discs to a media server NAS drive. Use media players loaded with Kodi or Plex in the other rooms. Simple. Effective. Low cost display-end tech. Doesn't tie up the main system either.
Am I definitely going to get issues with HDCP and EDID etc?
HDCP less-so unless you put something in the chain either deliberately or accidentally that stops the HDCP handshake. EDID issues are more likely, particularly when using so many (and possibly/likely different-spec) TVs. You can get EDID issues with the simplest 1:1 connections. Remember too, the system might work fine on installation, but what happens 5-10 years down the line when you've maybe changed three or four TVs. Will it work with the new hardware?
Ask yourself who really wants to watch the main Sky box in other rooms. Also, think about how you'll watch TV in the main lounge and kitchen-dining area. The chances are that Sky will be the go-to service; even if you have Freeview, most households with Sky use that almost exclusively, especially the non-tech inhabitants: Would you/they really be happy if some in a different part of the house hijacked use of the one Sky box?