Keep in mind that the performance increase will only be felt with multi-threaded apps, and likely only with those that can use the extra cores.
This is of course very true. Apps that are only single or lightly threaded will, individually see much smaller, if any gains. I won't deny 4C/8T is still very much a "sweet spot" today for many things performance wise (I love my 13" 2018 rMBP for example), it's just that it's now a budget/low power sweet spot, and has no place in a $3000 desktop computer. Furthermore,
1. With 6 and 8 core machines becoming (having become the) desktop mainstream, and AMD rumored to be pushing core counts even higher next year, an increasing number of apps will begin to be optimized to utilize more than 2-4 cores. If you're buying a machine today with the long run in mind, more cores is the smart buy IMHO.
2. Even when using applications that are only really maxing 1-4 cores/threads, having more cores keeps the OS/other applications running smoothly without slowing down or disrupting your primary task.
3. With the proliferation of smartphones and tablets for media consumption / simple usage, most people are doing more than one thing with their computer, the more you're doing at once, the more useful having more cores becomes.
4. As the OP said this is a family computer, that implies that it will likely face a wide and ever changing variety of use cases. Unless it just ends up collecting dust (a sad but very real possibility in 2018,) I don't think it's unreasonable to think that someone, at some point, will throw something at it that can utilize 6+ cores.
To elaborate a little bit more. I loved my 2014 5K iMac (4Ghz/4.4Ghz Turbo i7 4790K/M295X), it was super fast and a joy to use, such that part of me still regrets selling it. But if I still had it it would be approaching FOUR years old and yet, honestly speaking, in the CPU department, the machine OP JUST purchased isn't all that far off from a machine I bought back in October of 2014! Sure, the GPU/RAM/IO improved but, if it were my money, I'd certainly be voting (and have voted) with my wallet.