No, this is not why impeachment exists. A president is impeached for "high crimes and misdemeanors". If the Prez is acting legally, I can't see how he could be impeached for it.
Impeachment is a political process, not a judicial one. Trump was impeached twice, yet no legal charge was ever filed. All that is required is a willing house of representatives.
The impeachment is a political process but the impeachment proceeding is the legal process and Trump was essentially found not guilty in that process, although it was split among political lines so you could say they brought politics into a legal process.
Impeachment IS the process of brining charges against a sitting President. The House acts a very rough equivalent to a grand jury. The Senate trial is the court-room with Senators as jurors. The Senate chose not to convict, but charges were absolutely brought.
DOJ regulations pretty much prohibit bringing criminal charges against a sitting President.
Whether or not people think the impeachment process is a political sham is a different question/problem. Recently, it largely has been - both with Clinton and with Trump, for very different reasons. Even more so now with GOP members threatening to immediately impeach Biden (for what, I can't quite figure out) should they win back Congress.
Rather, this is what voting is for.