Very balanced post. Good analysis. Glad to see intelligence vs. everything India and India focused. You should write more in other threads. There aren't a lot of "balanced" posters on here from India.
Also, Iranians are independent, but there is "realistic independence" and "stupid independence". They are the later. A smart and most beneficial decision is the one made for strategic purposes, Iran lacks that "strategic partnership" view. While people running Pakistan come from global business background. They are ALL about strategic partnerships as all parties involved get something out of it (something that India did very well till Modi came).
Russians and the Chinese will get connected with Pakistan through the roads, rail and through the Ocean (airways already exist). Just between these three countries, you are talking 1.7 billion people within days of local drive. Now add Pakistan's influence on the ME / Muslim countries, you are looking at another seriously lucrative market for pretty much everything, with plenty of money. If there is any country who can make Saudi's and UAE buy Russian or the Chinese weapons worth a few billion, its Pakistan (a few billions is really a little investment for these countries like small change as they are filthy rich)!!!! So you have to see the bigger picture.
Pakistan is also a nuke power too and it poised to become a regional military power, and the top 15th economy within the next 10-15 years. Everyone sees that and knows that. Ten years from now, Pakistan's military and economic influence would be tremendously larger than today. So these countries want to form strategic partnership with Pakistan early so everyone reaps the benefits of Pakistan's growth.
"Independent" policy is neither a permanent phenomenon nor a virtue. For most part it is driven by circumstances.
Generally, there is always inherent rivalry between immediate neighbors (both land & sea) as they try to grow & pull the small neighbors around into their orbits of influence.
Pakistan- India, India-China, Iran-Russia, Iran-Turkey, Russia-Turkey, Iran-Saudi, Russia-China, China-Japan, Russo-Japan are some examples.
Alliances have their pitfalls too if not properly made and understood.
Pakistan being part of both SEATO & CENTO could not get any help in its wars with India as the aim of those alliances was to prevent the spread of communism from China and USSR - Not to fight India.
On the other hand India while being Independent (not being part of the alliances) was still cooperating with US against China in Tibet.
After wars of 1962 and 1965 with China and Pakistan, India needed strong support to with stand the rivals which resulted in the Indo-USSR treaty.
US itself sensed the irrelevance of SEATO & CENTO alliances and took advantage of the Russo-China rivalry to make an direct alliance with China to oppose the larger threat from USSR.
With Turkey, Saudi and Pakistan (all neighbors of Iran) having an alliance with US, it gave little room for Iran and was forced to side with Russia even though Russia and Iran had their own rivalry in Caspian sea.
Countries always face multiple threats and rivals but the alliances are made or broken based on the evolving threats, lesser of the evils and the benefits such an alliance would bring in.
No doubt Pakistan has played its cards very well and is currently being offered lucrative proposals by all the three super powers of the world to retain their influence in the country.