Sid Meier's games never aspired to be chess even when there is some strategy involved, the checkers approach allows for learning by doing, it's widely appealing and not very punitive/frustrating (unless you ignore long term consequences). The underlying game mechanics is based on basic arithmetics and statistics, it's much like an animated board-game really.
It's near impossible to have much depth (or smart AI) for all those different starting conditions. Hence there is a new focus on multiplayer...
There are many possible strategies, and the "one trick pony" is the player who insists on applying one strategy every time i.e. conquering europreans screws up relations with the natives (-1 you attacked our friend), more so if you keep their cities (-2 you have stolen our land). And I can see how the game becomes boring if you eliminated all competition early on...
The King's cash demands are there to prevent one player piling up gold, to buy a frigate or army and wtfpwn the competition, refusing to kiss the ring increases the chance of early tax demands (sinking the enemy caravel, will also increase tax for the victim), or on a more basic level to remind the player to always invest all his gold into new units.
Criticism is exaggerated and often emotional, which rarely helps the arguments but at least shows that people care about the game.