Trump promised to drain the swamp. It is common for a new politician to come in and want people to be loyal to the person that won the election. Trump has very different ideas than Obama had. It's important that Trump puts people into power who are able to carry out his ideals.
The country is in much worse shape under Obama, and the Democrats have proven they cannot be trusted with all of their scandals. I think that Trump should get rid of Obama's appointments so that the country can have a fresh start with new ideas and new personnel. We need a big change.
No, Trump should not fire Obama's appointments. The tradition is for presidential appointments to continue to serve until their replacement has been approved. By not continuing this tradition, Trump is ensuring that many important posts could remain empty for months. This does nothing to help the country, and only serves to deepen the divisions between Democrats and Republicans.
I believe that with so much of the country in turmoil over Trump's election, it is not wise for him to create stronger negative sentiments by doing away with Obama's appointments. Trump will need to earn trust and acceptance from those who oppose him and terminating perfectly capable appointees is not the way to achieve either.