I like it where it is. For many fans, the draft is probably more pertinent to their team's fortunes than the playoffs, and that's including some of the teams that make it. Waiting forever for it to happen to lengthen to "news cycle" like the NFL does is just torturing the fans.
These days people forget about news stories a few days after they happen, so even if the draft was later it's not like the Spurs would be getting so much coverage. Besides the parade, what is there really to report? The players pretty much go home and MAYBE appear on a few talk shows.