If you barely play games and if you play older titles (4 years or older), you could go for a GPU that is passively cooled. I try to get those card for workstations (as those shouldn't game at all), but also for personal use. They can handle quite some load and once I had one that had such a large metal convector mounted, that I could add a standard 80x80mm case fan onto it (once the owner started to complain that his system would reboot "at random").
A "there, I fixed it for you"-solution? Yes, but it kept going for another 2 years. Likely it still works, but it is an AGP model.... I am not allowed to throw away anything, unless approved.
Case fans are easy to come by and easy to replace. GPU coolers are not. Getting a second hand one for donor purposes, you should ask how much those donor fans had to work, before the chips gave out.
New passively cooled GPUs usually come with (much) smaller metal convectors, so extending "life" by adding a case fan is often not an option anymore. But my boss is getting a 3D printer and when that thing works, options will be back. That is to say, I can live/work with a PC that has fans working at full power all the time. Because that is the thing with case fans, not all models come with hardware that allows their RPMs to be adjustable. Just 'not at all' or 'full on, baby'. That I more often than not use a headphone when working, sure helps in that regard.
By default, GPUs in desktops (towers) have their fan(s) point downwards. Which is not the most ideal position, as air is sucked into the card, heated and then blown out to the bottom. Dust particles in that air can and do collect inside the GPU cooling fan(s). And dust tends to stick to fan blades too. With enough time, those cause an imbalance that becomes worse until you actually start to hear it. By that time, it will be very hard to get those fans back in proper working order again. By taking those fans apart, it is also not a given that their construction allows you to put it back together again in a proper fashion. The times I have tried, it was always working well for a week or two, but then problems would be back, often with a vengeance.
GPU fans are often small and of an irregular size, even between models from the same manufacturer. Replacement or repair isn't always an option. So, most people go and buy a new GPU. Meaning there is no incentive for NVidia or AMD to give a hoot about repair/replacement of GPU fans. And in countries where you can get replacement parts easily, who cares...
Here in Paraguay, Amazon, Newegg, Ebay and the like are not an option. It can easily take 3 or 4 weeks for things to arrive from the US at the PY border and your order gets slapped with a border "tax" that can be ridiculous. Given that there are not many stores in the capital that sell PC hardware. The few that do, charge a lot. So much, that if you have need for one or more parts that costs you 200 USD or over, you better take a vacation day and take the bus to a border city about 450 kilometers away from the capital and go buy parts there. Yes, the price difference makes it worth to travel.
A time-sink this huge, that is always a possibility though, so repair is still a thing here in these parts of the world.