Your experience is a perfect example of why running an INR higher than needed is not always the best choice. Your BPH is the cause of blood in your urine but it is exacerbated by your lower coagulation level. You probably still have blood in your urine, but cannot see it due to your lower INR.. For me the amoxycillin I have to take for dental cleanings gives me blood for a couple of days afterwards even with an INR 2-2.5..
Our body's built for an INR of 1, keeping an INR within range instead of running high is more "natural"
Ingesting the minimum correct amount of drugs necessary for a therapeutic effect is a good way to approach ingesting physiologically active or psycho active chemicals. Remember all drugs have non-therapeutic effects aka "side" effects but drug trials are focused on therapeutic effects, collection of other non-therapeutic effect data is not as comprehensive.
What IS a perfect example is trying to use an exception to prove a rule. Because ONE person had hematuria, you seem to conclude that EVERYONE with an INR above 1.5 WOULD have blood in their urine. What if this person had a urinary tract infection, and the warfarin made bladder or kidney bleeds show up?
What if people take your advice, and shoot for an INR closer to 1? We would see more strokes and pulmonary occlusions in people with prosthetic valves. Great advice.
As far as 'all medications' having side effects, this, too, is just plain wrong. Most of the stuff we eat, drink, ingest (as medications or supplements), or have injected or infused, may have side effects. If you consider food to be a medication (after all, if we don't have food, we will eventually get sick or die), then TOO MUCH food might have the side effect of diabetic shock (if you're diabetic), or weight gain, or many other things.
If you consider vitamins to be 'medications,' in many people, the necessary amount will be extracted by the body, and the rest would be flushed out. If you take too much Vitamin A, the side effect could be a yellowing of the skin.
But not all 'medications' have side effects.
For example, the effect of warfarin is longer clotting time. This is the EFFECT. not a side effect. Side effects often result from things made in the pills containing warfarin - not the warfarin itself.
Overuse of warfarin may have a 'side effect' related to what it does. If you take too much, you can have excessive bruising, bloody urine, and, if you take way too much, internal bleeding and other nasty (and potentially fatal) stuff.
But NOT ALL medications have negative side effects.
(In fact, some have unexpected, but valuable side effects. Minoxidil, probably still used for some heart conditions, had the side effect of causing hair to grow. It's marketed under the brand name Rogaine, and generically as Minoxidil. Similarly Proscar, a medication for prostate issues, also caused hair to grow. A dose that is 1/5 that of Proscar is called Propecia. I'm sure there are other drugs that have similar unexpected, but beneficial, side effects)