While the elections and interregnums were a time of major dysfunction, they weren't the main cause of the PLC's difficulties. At least in my opinion.
The main problem was that the sizable noble class (which was about 15% of the population I think) had a great deal of privileges, tax exemptions, legal protections, and opposed anything that threatened those privileges. They also owned most of the land, had most of the wealth, and just overall the power. The Golden Liberty was for them. The peasants and bourgeois had limited rights. The nobles opposed any taxes upon them or or demands to provide military services that could have allowed a professional army, instead utilizing an increasingly inefficient call up of the noble knightly classes (I forgot what it is called) that they demanded concessions to actually form while simultaneously using it as its basis for the privileged position of the nobility. The PLC, the largest state in Europe in its time, had a continuously standing army of like two or three thousand in 1600~ because of this, and it was maintained by a tax on royal lands. The nobility soon made its preference for foreign candidates for king, as they'd be out of their power base and thus unlikely to found a strong dynasty in the PLC. A move that often ended up entangling the PLC in foreign affairs. The nobles opposed rights for peasants or bourgeois as it would threaten their hold over them. Finally the big one, the liberum veto allowed any of the Sejm deputies to basically put a halt to the entire legislative process of the entire country, a fact utilized by their neighbors via bribes.
People generally focus on increasing the king's powers because that was the general trend of the time. However in reality what was absolutely needed for any functional PLC was the curtailing of the power, privileges, and monopoly on power held by the szlachta nobility. The constitution of 1791 that actually had a great chance of succeeding besides establishing hereditary monarchy focused on providing rights for the bourgeois and peasants, and banning the liberum veto. Yet even this was too much for many of the nobles, who then sided with Russia and waged a war to put an end to these reforms. This all but led to the Second Partition. They didn't want a reformed state. They wanted a return of the Golden Liberties, and a modern (at the time) state was not conductive to that.
So simply removing the kings won't solve anything, even if many of the kings were ineffective. The nobles were the problem, and reforms to curtail them would either be fought by them or could lead them to searching for foreign support in 'reestablishing the true PLC' like they did IOTL. Course it's possible to reform the PLC, but just removing the king isn't one of them.