Placing a value on UA miles is of course a personal decision, but 2 cents per mile is pretty reasonable. There are a few holes in your reasoning here, though. I'm just going to do the math for a single pax since I find it more tractable.

"Best" use of miles: saver 3-cabin First awards, 160k-220k miles. It's extremely rare to be able to do this for less than about $8,000 cash (and frequently much more expensive). But this logic only really holds if you derive value from flying F instead of J.
"Common" use of miles: saver Business awards, 120k-140k miles. Your $8,000 price point for a Business ticket is not really a fair comparison. While it is possible to be flying on an award ticket when a cash ticket is $8,000 it's very unlikely. For the amount of effort spent getting a family in a Business award like this, you could have spent the time to buy cash tickets in the $2,xxx range. This is roughly where I would derive a value of about 2 cents per mile.
Acceptable value: miles+cash upgrades. A good fare is going to be about $500 to Europe in K class, so once you include the copay it's $1,600 + 40k miles. This is pretty similar in value to a Saver award, but it requires (a) a good fare to start with, and (b) R space on United metal only. While an upgrade is easier to get than a Saver award on the same flight, you can leverage the Star Alliance network for awards which gives you overall a lot better availability.
Poor value: Common Economy redemptions. You can get to Europe for $500, or you can pay 60k miles for an Economy award. That's less than 1 cent per mile.
Niche value: When you absolutely have to travel. A Standard Award is 310k miles to Europe in J, but if you have to travel, it's also last-seat availability and those 310k miles could be buying a seat only available in full J for $14,000. Similarly, you might have access to Saver Economy awards when needing to travel on last minute notice where advance purchase means cash fares are sky-high. Maybe you pay 25k miles to do a domestic round trip which is $1,250 or more. These are high value but very situational redemptions.


Hopefully that provides some perspective.