It is 100% false that prosecuting current and former politicians strengthens law when we're talking above a certain low threshold of corruption. In those cases, it's up to the ruling class to police its own by using the legal code against low-level political figures and officials. The Chinese Communist Party operates this way more overtly but same principle. The incentive to do so is to strengthen the legitimacy of that ruling class, not because the law says you must.
According to the Law, you and I are committing "Three Felonies a Day". If the law were en vigueur then you and I and everyone else would be prosecutable 1984-style. It's at the whim of The Prosecutor to decide whether or not to pursue. Sound good to you? Me neither. The only thing stopping that is politics. When the political will is on the side of prosecution, then there will be prosecutions. We saw this with some heavy-handedness during the early days of the GWOT, 2020, Covid, hate speech legislation, many such cases.
The point being, interpretation of laws is a point of political conflict, often very sharp-elbowed. Even in the cases where laws are unambiguously stated (rare), there's still interpretation of the evidence, which doesn't happen in a political vacuum. Who would disagree?
You don't have to look far in history to see the abuse of the legal system in politics. Watergate is a prime example. Uninformed people think Nixon committed crimes and had to go. Anyone who spends just a little time looking at the details of that episode understands it as a political coup executed using lawfare. Whatever you think of Nixon's politics, the facts support that he was taken down by the anti-communist hawks in the defense establishment, largely in consequence of his opening up China. (The reasons were anti-USSR but given that China subsequently went from an agrarian backwater to a global competitor, one could debate whether they were right for the wrong reasons.)
Impeachment as a check/balance was just recently burned in Congress as a political tool to remove a sitting president. Extremely shortsighted. Or perhaps it just exposed it as a paper tiger. I thought it was burned when it was used against Clinton but it was only singed. Now it's completely discredited and no one will take it seriously ever again. That's the effect of abusing the law for political purposes.
What happened to the Roman Republic was overdetermined, but the Senate's threatened political prosecution of Caesar is historically understood to have been a motivating factor in his "crossing the Rubicon". If they hadn't threatened him with lawfare, would the Republic have survived a little longer? Perhaps.