It is personal preference of course. But I would say it's worth it. The 900Mbps/Gigabit speed is the line speed into the property. When it comes to Wifi, that's going to vary on factors (walls, distance, interference) which includes equipment. Some routers, or distribution systems like Powerline (usually limited to about 150Mbps via electrical wiring of a house), or Extenders themselves may not necessarily have the bandwidth to transfer the whole 900Mbps. This is rarely noticed, or important, if the line speed is slower than the capability of the Home Network. But once you start getting faster "internet speeds", then you notice it. Another factor is the receiving device has to actually also have the antenna capability to receive such high speeds as well. Generally speaking, that would be Wifi 6 devices more so than Wifi 5 devices. You would notice for instance (all other things being equal) that two Tablets (e.g. iPads) of two different generations (one being Wifi 5 and the other Wifi 6) might get different speeds at the same location on the same network.
Wired connections are generally speaking the best and only way to get the full speed to the other side of the house. In the example you mentioned of your friend with BT 1 Gig and the PS4, if you're worried about something similar happening (or perhaps what he/she could do), you could either use some internal Ethernet like you mentioned. Or else, certain Mesh systems like the Netgear Orbi AX6000, Asus Zen XT12, Amplifi Alien etc, or BT's Whole Home Wifi 6, might be able to better get a lot of that 900Mbps line speed around the home. You could then wire in to the satellite unit to get a faster speed closer to the main Router speed (which is near the ONT). Those aforementioned systems use a dedicated band (well except for the Alien, but it looks cool) purely for communication between the internal network. It all depends on personal preference and convenience whether the homeowner can run internal, or external cables, or prefers wireless solutions etc.
I would say yes for £5 it's worth it. Now reading your post again, in terms of lag, I guess wired is the way. But at least wiring into a satellite would give you as good as possible a connection versus totally wireless.
As for the line speeds, whilst theoretically there is contention on the national network as a whole if multiple households were all gaming, or downloading video all at once, I do think the FTTP speeds in general are pretty consistent. Pretty solid full 900 here. At the moment, I think you have to go for your own Mesh system/wired solution though as the current (as of writing) Routers and Wifi offerings from the ISPs are not really designed for the 900Mbps packages. The fastest the home network can go will always depend on the slowest link in the chain between the ONT and your device.
