No acting president would want to use his influence to prosecute a former president/ rival candidate unless their actions were beyond the pale.
It'd be open season for every exiting administration and would get super ugly super quick.
President Carter didn't go after President Nixon, just like President Obama didn't go after the Bush administration for the Iraq fiasco.
If these people were too stupid to see that no president would willingly leave themselves open to return fire on their own exit, then they deserve everything that's coming to them.
Carter did not succeed Nixon. Nixon resigned and Ford assumed the Presidency. Ford was from Nixon's own Party.