Not really. Not even the US would have done well without a presidential term limit (which, de facto, was customary pre-Roosevelt as well - thanks to Gen. Washington). In a presidential system of the American (drop the Lat) type, the incumbent's advantage is simply too strong. True, in the US incumbents, occasionally, loose - but most political scientists agree that they don't do so frequently enough. Without the de facto (originally) or a de jure (now) term limit you'd observe lengthy periods of single-person rule. Frankly, I am pretty confident that in the absence of the two-term tradition even the US would have lived through a few coup attempts in the 19th century, and, may be, a couple of extra civil wars.
Considering that between Jackson and Wilson we had exactly one President serve to the end of a second consecutive term, Grant, with one term Presidents between Jackson and Lincoln not even getting renominated by their own party, I think you're completely wrong about the prospect of a 19th century U.S. coup d'etat. The Union dissolving as it did in Central America and Gran Colombia is a far greater possibility than any coup d'etat to take control of the then weak Federal government. If that had happened, we'd probably have had some coups.
