Why was 幸 simplified to 扌in 報(⿰幸) to 报(⿰扌)?
As with many simplified characters, cursive scripts (Caoshu) can be informative.

In "Chuyue tie" by the famous calligrapher Wang Xizhi, 報 is written as follows:



As @dROOOze mentioned in the comment, the radical 幸 came from the character for handcuffs, which could indicate that the use of 扌(手) might related; but I can't find any source for this so far.