In the country (as opposed to the city) everybody knows what everybody's doing, there are always a ton of witnesses, who went to whom, who sleeps with whom and so on. If Sir Henry died anywhere near the Stapleton house let alone in it, the latter would be the primary suspect and even the lack of evidence due to rudimentary forensic expertise in Victorian England mightn't be able to save him. And sure the truth that Stapleton is Baskerville would be uncovered and after that any body of jurors would send his ass straight to the gallows.

As for the trouble of using the dog, see it that way: it worked once, it may well work twice, makes perfect sense.