The point of Napoleon's invasion of Egypt was just such a strategy you proposed. He was planning to overthrow the Ottomans and perhaps push on to India, thus threatening Britain's chief possession and perhaps forcing them to quit the war. The fact that Nelson destroyed his fleet, put an end to that attempt. Thereafter, once the Directorate and his Consulship had been wound up, and he declared himself Emperor, his goals were different. Peace had been made with Russia at Tilsit, but the long term future of Napoleonic Europe was shaky at best, so long as Britain kept undermining the Continental System and willing to spend their cash in new coalitions. Russia needed to be neutralised, and as far as Napoleon was concerned, it was a massive success. Borodino was a victory and Moscow burned. The problem came that the Russians didn't sue for terms, which was what Napoleon was trying to achieve. He was attempting to force Russia to accede to his requirements, not to conquer it. This was why his army wasn't set up for a long term occupation, and why the Russian destruction of the countryside was particularly effective once the campaign dragged on longer than expected. The Russians won because they didn't cut their losses and held out, which had never happened before. The Prussians and Austrians, even Russia itself, had always come to the table after a Napoleonic victory before. This was his mistake.
Hitler did set out to conquer Russia. He failed because he constantly changed his objectives, first Moscow, then Leningrad, then Moscow, etc. and alienated groups that were his natural allies, like the Ukrainians, by racialist policies. Germany in WWI very nearly dismantled much of the eastern part of the old Tsarist empire by pandering to local sensibilities.
The Nazis could have won, if they had continued to attack Moscow and thus forve Stalin to flee. This would cut of aid arriving via Murmansk and made the fall of Leningrad only a matter of time. If they pandered to Ukrainians or Tatars in the South, they could form puppet states like Slovakia or Croatia, that could hold that line, up until they could drive for the Caucasus oil fields.
A drive through the Middle East was impractical. Firstly, they would need Turkish support or conquer Turkey. This would be unlikely or expensive to cross the Anatolian highlands. While they did have arab allies and a potentially helpful uprising in Iraq, their supply lines would be hopelessly stretched, and Britain could easily reinforce from India.
An attack via Egypt is also not feasible, as Germany struggled to supply Rommel, who himself nearly succeeded on this front. The problem is supplying troups over the mediterranean, especially when Malta was still in British hands. It simply made more sense to atrack Russia, who was anyway a looming threat - militarily, Ideologically and racially, to Nazi eyes. German control of Russian oil was also more economical to achieve, and if they held Russia, a drive down, bypassing Turkey or Persia, would also be in the cards.
Russia wasn't too strong to be defeated. The Nazis crushed them initially, and thanks to their own (or Hitler's meddling) inept handling of the campaign and silly policies towards natives, they failed. They could easily have won.
Napoleon did win. He just wasn't prepared for Russia not surrendering as everyone usually did, so he can also be excused somewhat. He should be castigated for not attempting a more orderly withdrawal though, and leaving so much to Ney. If he had, he could probably have kept his fortunes in Europe, and in the long run, the Russian serf state would not have kept up resistance indefinitely.
Russia has been conquered by land war - the Mongols did it and the Polish-Lithuanian Commonwealth managed most of European Russia. The Russian Civil War saw white Russian forces with foreign support control great swathes. That is my two cents on this topic.
