Doesn't really matter much who designs the Msjidul Haram. Let the nonmuslims be allowed to grow afiliation with Islam's holiest place, in some way. That might lead to changing their attitude towards islam and it's holiest place, resulting more non-muslims coming to Islam. Allah knows what's best for Islam & Mecca.
After all, Quran, Prophet Muhammad, Islam is not anyones sole property, all these were sent/given by Allah for the entire mankind.
[Post CWC15 Consistency Record: [B]Test: W-0 L-1 D-1/B]// ODI: W-3 L-0 // T20: W-1 L-0]