If a president breaks the law while in office, should they be immediately impeached and removed?

There is a gray area for actions that are later deemed illegal in the "overturned by courts" sense, but there are also actions that are CLEARLY illegal. For example, Trump's EO on the 14th Amendment will very likely be stopped in the courts but it wouldn't be called "illegal," but his firing of the 18 inspectors general might cross the line (similarly to what Nixon resigned over).

So if the president does something that crosses the line, should they be impeached/removed? Or should they just be allowed to continue on in their term?

NOTE: This is not a statement of whether or not the president will be charged with a crime, since all actions taken as president through the power of their office is protected by immunity. This is about the POLITICAL process and accountability.