With you overall, but given the toxicity of the fumes some quality / rated fume extraction might be the one area where cheap/self made item isn't worth it
If you're doing it a lot, then it's definitely worth making sure it works properly. If you're doing it occasionally, just make sure the area is well ventilated and you're not outright inhaling the fumes coming off the solder, and it's not likely to make any real difference to the health of your lungs.
"Well ventilated" on its own is completely insufficient. If you are soldering without any fan or extraction, you _will_ inhale fumes because you have to look right over your work when you solder, which is exactly where the fumes are.
In general, the danger with soldering fumes is not the average concentration in the room in which you're working over the duration of a session, it's inhaling the very high concentration of fumes right as the soldering happens.
We could debate how much damage this is going to do and whether it's worth worrying about, but there isn't really room to debate that ventilation alone is going to do absolutely nothing.
Well ventilated area + fan is probably okay, but you need the fan right next to your soldering iron or it needs to be a gigantic fan otherwise, again, you are just going to inhale most of those fumes.
I had to read your comment a few times to understand the confusion.
The issue is that you've concluded that a $50 fume extractor qualifies as spending real money, when in fact you're still well into the realm of cheap and crappy. What you're describing is quite literally a PC fan blowing into some foam. It's better than nothing, but you'd still be better off with a [real] fan and an open window.
Good fume extractors cost real money yet will seem very cheap if you are running the numbers while waiting for a chemotherapy appointment. JBC makes several, and they are FAR from the most expensive available:
Its your life, but IMO you really don't want to fuck around on this detail if you plan to do a lot of soldering. You might not care, but there could be people who love and rely on you to not try and to save a few hundred bucks on the thing that keeps you from premature death.