Well it's a "your mileage may vary" kind of anecdotal thing. Technically, what you say is true. The makers of viagra have never claimed an increase in penis sensitivity. But take for instance men who suffer from retarded ejaculation. A symptom of re these men complain about is a numb penis which prevents them from reaching their orgasmic threshold and ejaculating. Now this numb penis thing is really all in their heads. But, when these men are prescribed viagra many claim increased penile sensitivity.
Now this could be some kind of placebo effect. I think what you said about
getting and staying hard may be the key to this reported increase in sensitivity. Getting and keeping an erection is just one less thing to worry about and in retarded ejaculation and psychosexual erectile dysfunction, performance stress is one of the leading causes of the dysfunction.
Placebo effect or real, physical increased sensitivity, it doesn't really matter as long as it works.
In the case premature ejaculation, any kind of increased sensitivity placebo or real will cause problems. An erect penis is more sensitive than an unerect one so that in itself may cause trouble.
But like I said it's a your mileage may vary type of thing. The original poster should get a free sample of viagra and give it a try. If it works great, but it may backfire.