According to the concept of the imperial presidency, before the new deal the office of the president of the US was far less important than it is today. With the rare exceptions of Jackson, Lincoln, Teddy Roosevelt and Woodrow Wilson, few presidents before FDR truly expanded the office or used it as bully pulpit. Most presidents were insignificant (often one-termers), and unlike today the office wasn't particularly desirable as it had none of the powers to set domestic agendas, control domestic programs, and lead the free world. The founders had put congress first in the constitution and set out its role far more accurately intending that that branch would lead government, only giving the president executive and military roles because they knew the father figure washington would be the first to take the role.
If this is true, then why did anybody want to be president before 1930, surely it would be seen as an irrelevant largely powerless office within a political career? yet three of the founding fathers after Washington sought the presidency as the best place to pursue their political energies, and throughout the 19th century there was vicious competition to be president, with expansive campaigns and political parties orienting their entire conventions around the quadrennial race, and often having long contested conventions to decide a nominee. Essentially, if being president was less important being in congress why did so many men, seek the presidency before the 1930s
The first five presidents were founding fathers and their terms in office were seen as continuations of the revolution they helped foster. Each had bona fides from serving in state government and then as cabinet members were seen as being groomed for the presidency. The sixth president was John Adams’s son who had served as ambassador and Secretary of State and actually lost the 1824 popular vote to Andrew Jackson, who was the first real outsider to be elected president in 1828. He ran as a hero to the lower class being denied a voice by politicians (an argument strengthened by his loss in 1824) and bankers, long hated by southern farmers. Jackson campaigned directly to the common man in a departure from the approach of his predecessors and was emboldened by his mandate. He is a standout of the era for his dominance in office going as far as to override the Supreme Court. Jackson’s Secretary of State and protege Van Buren was elected next but was less successful, followed by a war hero Harrison who died a month in, and John Tyler, who became president by accident and served only one term.
That was the start of the streak of presidents who faced issues surrounding slavery predominantly but were either too weak or unwilling to confront the problem until a republican was elected in 1860 on the basis of constricting slavery following the John Brown raid and Dred Scott decision. Lincoln embraced the role of leader of the federal government, not just executive branch, and the president’s incipient power to wage war to preserve the union. After his assassination, congress reasserted itself by impeaching the next president, Andrew Johnson. Ulysses Grant was extremely popular for his winning role in the war but embroiled himself in scandal as president, drawing the influence one man should wield in office into question. Presidents between Grant and Teddy were mostly ineffective at the pressing issue of reconstruction and racism but found success in other arenas, provided they were not assassinated (Garfield, McKinley).
As the revolution faded and political parties gained traction, presidential nominees were chosen based on their appeal to voters more than their credentials. So war heroes like Jackson, Harrison, and Taylor were championed. Slavery and the various concessions made by northerners also determined candidates and their electoral college margin of victory, so it was not completely a matter of who wanted to be president as much as who white men would elect. Many presidents pre and post 1930 were reluctant like Grant and Truman or expressed regret like Adams and Taft.
The presidency is different today than it was in the 19th century but the appeal and power of leading an energetic nation has always attracted men.
Edit: *constricting
Sources: founding brothers by Joseph Ellis, Jacksonland by Steve Inskeep, American Ulysses by Ronald White, battle cry of freedom by James McPherson