I think to lay out the implications of Alexander living longer you have to understand that by 1820 he was in the midst of what would be today be diagnosed as a deep clinical depression. Some modern scholars even claim his behavior resembled schizophrenia in certain aspects. It is no exaggeration to say that it was a major reason the junior officers who became the Decembrists were so emboldened in their plots* against the government. Years before his death, Alexander had been warned by several senior officers that there were advanced plots by certain elements in the Imperial Guard to overthrow him and murder the members of the Romanov dynasty to establish a republic. The Emperor ignored all of their pleas and allowed the would be rebels to continue to gain influence.
If Alexander lives 20-30 years longer than he did in OTL, then this is going to come to a head at some point, and it will be far worst than the Decembrist Revolt was. That coup was launched because the more radical leaders panicked when Alexander died and thought their best chance to succeed in their plans was to strike during the troubled first days of Nicholas's rule. Under this proposed scenario, they would lay low and no doubt become even more entrenched in the highest levels of the Empire's bureaucracy. Alexander's passivity in this case might lead to something like the coup that overthrew Pedro II of Brazil in 1889, but it could also explode into a full out Civil War if Nicholas and more reactionary elements in the government have enough support available to them to stage serious resistance.
Regardless of this possible outcome, Alexander's mental health would most likely continue to deteriorate under the stress of managing the government, which he had come to see as an onerous burden. If he has a full mental breakdown and a regency has to be established, it would cause a political crisis, and could also cause a civil war to break out. There was no mechanism in place for the Russian government to make provisions for an emperor who had not died yet was no longer capable of ruling. It would be infinitely more messy than the confusion over the succession that broke out in OTL, and cause everything in the Empire to come to a screeching halt for an extended period of time; two or three months at a minimum. The Polish Army might even decide to time its revolt against the Russians to take advantage of the chaos and have a much greater chance of winning independence, or really muck things up by forcing the Prussians and Austrians to get involved with an invasion in order to keep their own Polish territories secure.
For all of the invective hurled at Nicholas I by his critics (a lot of which is deserved), he was the man who ordered the organization of Russia's first modern written legal code and and set up the mechanisms for the smooth (if heavily micromanaged) flow of authority from the Throne to all of the offices of government. Also, his aggressiveness in foreign policy which backfired on him during the Crimean War proved to be very effective in the early years of his reign, greatly expanding Russia's territory and influence in the Caucasus, Central Asia, and the Far East. His heavy-handedness in Poland caused a revolt, but also oversaw its quick and efficient suppression. He was a man of energy and action, and in the 1830's and early 40's that was the sort of leader Russia needed. It also could have used a leader who was not so thin-skinned, insecure, inflexible, and unable to embrace new technologies, but I am not so convinced Alexander would have been much better in that regard. If Nicholas had died at forty-seven like his brother did he would most likely be remembered far more fondly by history than the currently accepted view.
That is my take on it at any rate, but I focus a lot on the personality of the subjects involved and perhaps do not take into account the greater social forces around them.
*Tolstoy dramatized the deep feeling of discontent among the gentry and intelligentsia at the Emperor's seeming disconnection from the everyday concerns of ruling his empire in the very last chapter of War and Peace