The NBA may be following the NFL's lead and pushing back the Draft under the guise of "creating more interest" in the Draft, which is...well, about exactly what you'd expect to hear.
This year's Draft on ESPN drew a 2.0 rating and 3.0 million viewers, the second-best marks in recent history. The league reportedly wants to create more space between the NBA Finals and the Draft, due to the hangover of the Finals seeping into the Draft and sucking the drama and excitement out of it.
Of course, the main issue with pushing the Draft back is that it would also push back the beginning of free agency and the summer leagues. And honestly, do we really need another week of Draft coverage? The lottery is what people are really interested in, and teams that are in the Finals (or hell, deep into the playoffs) really have no dog in that race (barring some silly trades, of course). It almost seems like this is something being spurred on by the major networks so they'd have something else to talk about in July aside from baseball and the start of NFL training camps in a month.
The Draft does not need any more lead-in time from the Finals. The NFL can wait awhile between the end of the season and the Draft because their season is over in five months, including the playoffs. The NBA season ran from November until the end of June this year. That's eight long months of basketball, and the college prospects that were drafted haven't stepped on the court since mid-March to the beginning of April. Adding another week or two would probably have the adverse effect from what the NBA thinks will happen.