Quoting russell@coker.com.au (russell@coker.com.au):
Removing Tony Abbott did not involve admitting that he did anything particularly wrong (specifically no criminal acts etc). It merely meant that most MPs in his party thought that there was someone better able to do the job.
Such is one of the strengths of a Westminster-like parliamentary system. (As you may recall, I'm anglo-centric on account of personal history, though not anglophile. So, please forgive my starting assumption that parliamentary systems resemble the Mother of Parliaments in Westminster until proven otherwise; I'll admit it's mental laziness. My thanks to Trent for his mention of the Oz framework's 'washminster' nature, which I look forward to reading about.) By contrast, the USA provisions for removing many Federal officials from office (particularly, Pres., VP, and Federal judges) is complicated. The Constitution specifies that accused must be found guilty by a majority Senate vote of 'high crimes and misdemeanors', a phrase not anywhere defined. Scholarly consensus is this phrase has ultimately a meaning defined only by political will, however. The USA governing framework is very odd and 18th C. experimental, which I've tried to account for to European friends as what happens when a collection of dissident Brits have a mad afflatus to craft a novel government based largely on abstract, unproven ideas from a French philosopher (Montesquieu). Thomas Jefferson openly expected the US 1788 Constitutional framework to last maybe a score of years and then need to be junked and replaced, by demand of the citizenry, perhaps with more bloodshed, so one can say this antique contraption has long outlasted its expected service life already (with help from patches).
If members of Congress were able to vote "we think Paul Ryan is more capable as President" instead of "we think our President is a criminal" then maybe things would be different.
Quibble: If the Senate were to vote _only_ to remove The Toddler, and do nothing else, then (current) Speaker of the House of Representatives Paul Ryan would _not_ be next in line for the Presidency but rather Mike 'torquemada' Pence, the VP. Here's a hilarious political fantasy: Impeachment and trial gets delayed until after the November midterm elections. The Senate finds cause to remove _both_ the Pres. and VP. (This assumes the House files indictments aka impeachmens against both, and the Senate presumes to find them convincing.) Let's say for further entertainment value that Hillary Clinton has run in the November midterms for a House of Representatives seat in (say) a New York State Congressional district, and won. Let's say that the Democrats achieve an absolute House majority in November, and then elects as the new Speaker of the House... Hillary Clinton. Guess who then would immediately ascend to the Presidency upon Trump and Pence's removal from office? ;->
Finally while most Australians think they are voting for a PM, what they don't realise is that there's nothing stopping MPs from voting for someone different immediately upon entering Parliament.
This was also true in Westminster, and is how Theresa May replaced David Cameron without a nationwide election -- based just on an intra-Conservative reshuffle. Oz gains many advantage in electoral flexibility from its pioneering use of ranked-choice voting, I vaguely recall. Such methods have been slowly gaining more adoption in more progressive-minded parts of the USA, such as (locally) the City of San Francisco. Adopting it for Federal offices would of course required Constitutional amendments, hence would be very difficult, more's the pity.
But having the US President at odds with Congress seems a common occurance after mid-terms.
It's actually so common that it's expected. Rare is the party in power that doesn't raise a backlash after a few years.