Yes. Exactly. And sorry if I earlier may have been insulting in my delivery.
But in reality, the People (House) can impeach for whatever they determine is impeachable. It can be, "Hey we made a mistake with this guy!". There were no federal U.S. statutes at the time the Constitution was penned and ratified, because the government was yet to be formed! So there are no defined "high crimes & misdemeanors". When the President is charged with something like "Abuse of Power", that itself is the crime.
Well, yes. The founders set this up so it would be easy to charge the President, but difficult to remove him. And they specified that the Senate Trial, though not the House investigation - except for the impeachment vote, to be made public.
The rationale here seems to be it is relatively easy to investigate & charge in the House, where the charges then become made open to the public with a trial further enlightening the public in the Senate, requiring a higher bar for removal after the evidence has been heard byall in the form of a trial. So in essence, the "People" complain and the Senate takes a close public look at it with a high bar. Quite honestly, I think it's a great system.
Now as to opposing parties impeaching in the future, that will have to be determined. But impeachment is the ultimate political expression of the People. And in this case by putting Dems in charge of their House, it seems to be the will of the People. The will of the People will ultimately prevail regardless, though. If the People's will was not for their House impeaching, the People will remove those impeaching representatives from office. So 2020 House races will tell you exactly how the citizens of the country are feeling about this!
But I'd like to close with one more note. The House more accurately reflects the distribution of the citizens, than does the Senate or the results of the electoral college. This was seen in 2016 with the differences between the EC & popular vote totals. Quite frankly, this is why we see such political differences between the House and Senate. And it may continue if Trump wins the E.C., but loses "the People" again. In that case, I don't see anyway for there not to be further conflict.