Consider the most obvious alternative. Obama had no interest in Carter Page, his objective was to find a way to insert a government surveillance operation inside the Trump campaign. The easiest way for DOJ and FBI to get what Obama wanted was to take a patsy like Page, lie to the FISA Court, and walk away with a FISA warrant.
Page was known to the DOJ, as he was involved 2013-2015 in FBI investigation which led to Russians charged with spying in 2015; and, admitted an undercover role, providing subsequent court testimony. His role ended spring 2013, six months before FISA allegations surfaced.
http://online.wsj.com/public/resources/documents/2015_0126_spyring2.pdf