I was being mostly sarcastic with my "why not just..." remark. While 50%+1 may prevent legislative overreach (as with any voter-passed initiative), it's still a terrible barrier for a constitutional amendment because I have no faith that a simple majority will vote to protect or expand the rights and privileges of a minority. e.g. California's Proposition 8 (an amendment banning same-sex marriage in 2008) passed with 52%.

My point was that, if the amendment threshold were 50%+1, it seems in the interest of anyone seriously wanting to pass an initiative through the voters would want to make it a constitutional amendment simply to prevent it from being declared unconstitutional by the court. That's basically what happened in California -- Prop 22 (an initiative banning same-sex marriage in 2000) was struck down in May 2008, then Prop 8 was introduced in June with essentially the same language at the constitutional level.

Granted, Prop 22 passed with over 61% and support for the ban dropped about 9 points in the 8 years in between, and some of that may have been because of the difference between statute and amendment. But I still feel we need better protection of minorities than "majority rule", especially when called out so specifically in cases like this.