In theory, the Speaker of the United States House of Representatives is the third-most powerful person in the country. Voted for by the entire House, but traditionally coming from the majority party, the Speaker has a wide array of responsibilities, including bringing legislation to the floor to be voted on.
This is in stark contrast to the role of Speakers of the House in other countries, where they are typically neutral and their main duty is to make sure that the process of legislating is carried out in a correct and civilized way. But more recently, the office has been one that many would want to avoid as its powers have become limited by things like rambunctious caucuses.
Hard-line wings of the party make it almost impossible to govern
When John Boehner became Speaker in 2011, it seemed like it could be a cushy time for him as the Republicans held a newly-acquired massive majority in the House. However, around the same time, a faction of the party that called themselves the Tea Party Caucus rose to prominence. Made up of members of the far-right wing of the party, the caucus seemed dedicated to sabotaging any piece of legislation in which there was any sort of compromise made with members of the opposition and afterwards going on cable news and complaining about how so little gets done in Washington.
The Tea Party Caucus has largely given way to a similar group called the Freedom Caucus, but the results have mostly been the same.
On the flip side, far-left and other groups have started forming among the Democrats that would likely be a source of frustration if their candidate held the gavel.
Speakers take more than their fair share of the blame for the problems in Washington
After the Freedom Caucus drove Boehner to an early retirement in 2015 and the heir-apparent in Kevin McCarthy was forced to withdraw after a bungled television interview, it fell to Paul Ryan to take the post.
Ryan clearly understanding the problems that come with the position in modern times, very much did not want to take the job and had to be essentially forced into it. He would not only be met with the Freedom Caucus and the fierce opposition of the Democrats, he would be left to deal with a new problem - President Donald Trump.
While Ryan has been quick to condemn many of Trump's most morally objectionable statements, including his derogatory references about places like Africa and Haiti, many on the left seem unsatisfied. In fact, they would probably not be unless, maybe, Ryan became nothing but a full-time critic of Trump and led a full-out rivalry between the Legislative and Executive Branches. Which, if one actually stops and thinks about it, is probably not a good idea.
Similarly, criticism has been pointed in Ryan's direction for the lack of action taken by Congress on many pressing issues. Case in point - gun control. The need for gun law reform was in existence long before Ryan's tenure, including when Nancy Pelosi was Speaker and the Democrats controlled the House, the Senate and the Presidency.
Frankly, they didn't really put much of an effort into it. But even if Ryan put his full weight behind it, coming up with any major meaningful legislation on the topic that could pass both the House and the Senate and be signed into law by the President is exceptionally unlikely. And Ryan hasn't wanted to waste time and taxpayer money on something that doesn't stand a chance.
In the end, maybe the biggest criticism of Ryan is that he has been too practical. He isn't perfect and there have been times he should've stood up to Donald Trump more than he did. This has been noticed in his district, Wisconsin's 1st, where his formerly safe seat has been put in play and it was suddenly an open question as to whether or not he would even be sent back to Congress. He has announced his intentions to retire and it's unlikely that whoever his successor is, whichever party they may be from, will fare much if any better.