This is exactly what happens with both parties. It's a byproduct of the party system.
Republicans: small government, better business environment, etc
Democrats: strong social safety net, everyone pays their fair share, etc
Athenian offices were strictly term-limited, except for the position of general. People apparently felt that having military experience in that role was more valuable than the benefit of term limits would make up for, and it's hard to blame them for that.
But the general, able to serve for life, the only island of stability in the government, accumulated all the political power. This mostly defeated the purpose of having term limits on any office.
American presidents are term-limited, but American political parties aren't, and policy -- in terms of the solutions, but also in terms of the questions that get asked -- is set by the parties. I think this is more than just a coincidence.
On the other hand, Senators and Congressmen are not term-limited, but they don't seem to accumulate much in the way of political power.
(Also, senators are congresspeople.)
Maybe so, but "Congressman" is the title for someone who sits in the House of Representatives, while someone who sits in the Senate is a "Senator".
The Republicans are far more unified. It is both their strength and their weakness.
Or not. What about the Trump faction vs. the RINO's.
Republicans are split: libertarian, nationalist, religious
There are factions in the Republican Party, but for various reasons they are much more prone to have the non-dominant faction submit meekly to the dominant faction in terms of most actions in government, and even most public statements outside of contested primary campaigns. And even there the actual policy disputes are often not front and center.