I currently have all three cards you've mentioned. I've used the United Mileage Plus card on several occasions to redeem flights and you're right, even with advanced booking (more than 7 months in advance) the seats available for purchase using miles (not "upgrades" but full purchase) are very limited. They are especially limited for seats on Star Alliance partners (for example, Lufthansa) and are less limited for actual United flights, since the miles are actually United miles after all.
For most programs, the points or miles value are about $1 = 100 points/miles, meaning, 50,000 points/miles equals about $500 dollars worth of purchasing power, whether you choose to redeem them for products from the program's online mall or travel (such as flights, hotels, car rental, etc.). Just checking United's mileage redemption chart, a round trip flight in economy from the US to Europe costs 60,000 miles (this is their "Saver Award", which is their cheapest award ticket), which when translated to dollars, is $600. A round trip flight in business costs 115,000 miles (140,00 miles if on a Star Alliance partner airline), which translated to dollars is $1,115. So while mileage-wise, business costs a little over double the cost in miles, in reality if you were to pay cash for a business class ticket, it would cost a lot more than double. Just checking Lufthansa's website, a round trip business class ticket between San Francisco and say, Frankfurt, STARTS at $5,000-6,000.
So where the United Mileage program really shines is when using the miles to redeem a seat in business class. Because while I can personally afford a $600-$1,000 ticket in economy rather than use my miles, I couldn't afford a $6,000 business class ticket, nor would I be able to find a business class ticket for $1,115 (or $1,400 for a partner airline).
As for the Chase Sapphire and Capital One cards, the miles are not tied to any airline mileage program. Instead, their miles can be used to: reimburse travel expenses you've incurred on that card, purchase goods from their online mall, transfer to a mileage program, or used to book travel through the cards own online booking website. For Chase Sapphire when you book through their online website using your miles, there is a discount of I think 20%.
I think it's good to have both a card that earns miles directly for an airline program and another one that is not tied to any program.