Mixed feelings here...
Fans just vote for who they know. You'd see stupid guys get in before much better players. "homer" voting if you will. Happens to anything you let the fans vote on. All-Star Game? Plenty of guys who don't deserve to be there get in due to name recognition alone...NFL rookie of the week? Even if you're the 5th best guy, if you're a brown, you're going to win because the fans here vote constantly, etc...
BUT, I think something has to change so that some of the overlooked players can stop getting disrespected. Maybe after every year's HOF entrants are named, THEN you let fans vote on a pre-selected group of guys. This obviously wouldn't be high-profile players, it would be guys who get votes every year but just can't get enough to get in. This would keep everyday fans from caring, but still get the results...