Old? Well, that’s relative.
Stupid? Certainly not!
Being well-located, with lots of airline options … that’s something to consider further.
Starting from O’Hayre gives you choices, with or without having/using Miles. How much competition do British Airways and American Airlines have in Chicago? Denver International Airport has more options now than back in the day, with British Airways, United, Lufthansa, Icelandair, and just recently, Turkish Air all flying direct to Europe. I’ve only got Miles with one of those, BA. Any route other than a direct flight from Denver means extra money (and time and energy) to connect at at least one additional airport. Some flights are better deals than others.
Flying from the “Basel” Airport (which is in France !) to London in a couple of weeks is going to cost 9,000 Avios plus $1.00 for one person. That’s pretty good. Then, the flight back to Denver from London will take a lot more Avios and really a lot more dollars. But we jumped through enough credit card hoops to have earned a “Companion Ticket,” whereby two can fly for the price of one person’s Avios, plus additional fees for each person. Not two-for-one, and not everybody has someone to accompany them, but it’s better than full price! You can’t really equate dollars to Avios; it’s not a 1:1 ratio. But spending Avios means spending fewer dollars, although it’s not always a reasonable value.
As an example, in steerage, Denver to Warsaw round-trip for one person on BA next January will cost $664 out of pocket. Applying Avios will reduce the fare by just $24 for just 2,000 Avios, or up to $410 for 81,050 Avios. You get more discount per Avio (if that’s the singular) using 2,000 than when you use 81,000+. It’s diminishing returns, the more Avios you spend. But Avios don’t precisely equal dollars, and hey, if you can save $410 some way, it’s not the worst thing in the world. So it’s $664 out of pocket, or $640+2K Avios, or $254+over 81K Avios. Additionally, it would be $416+over 47K Avios. Perhaps that’s a clearer choice than what you described for ORD. Although if you’d jumped through credit card hoops to earn cash back instead of miles, perhaps that might’ve been a better reward. From Denver, the flight to Warsaw connects in London, then straight to Warsaw (after an overnight, which means sleeping in a plastic chair in the terminal, or at a hotel). Coming home means flying BA, Finnair, and/or AA, with two connections.
If Denver seems like possibly a better deal than Chicago, how much will it cost you to get to Denver? There goes your savings. Or, what if you paid some other airline to get you to Europe, then used miles to get onward to Warsaw?
Spend Avios or don’t, depending on whether it makes economic sense. A person who’s got experience and is wise will see when it doesn’t, and you’re already there.