Medieval government was very dependent on the personal strengths (or weaknesses) of the reigning sovereign. If the king was unable to act for some reason, perhaps because he was temporarily unwell, it did not take long for the structure to start to creak. It's true that there was a bureaucracy (the ancestor of the civil service) and a council (not quite a cabinet, but capable of taking some executive decisions on the king's absence) but the king's input was vital.
Richard came to the throne while he was still a child, and there's no doubt that he had been raised by his father, the Black Prince, with a very high estimation of his own sacred person and of the royal prerogative. In a sense this was not controversial - there was no questioning of the king's right to rule, or of his exalted status in the hierarchy. The first problem was that he never developed the broad relationship with the nobility that Edward III (for example) had enjoyed - one has the impression that he was on a slightly different wavelength to people like his Uncle Gloucester, or the Earl of Arundel. He preferred to rule through a clique of his own choice, not always giving his important relatives the power they thought they deserved. (Come to think of it Edward IV ruled in the same way, so maybe Richard wasn't that far out?)
The second problem was that he had an awful lot of relatives to satisfy, and there was no way he was ever going to make them all happy. Medieval politics (if not politics in general) was ultimately all about the control of patronage, the gift of land, offices and revenues. The available pot was very small, and Richard had a nasty habit of giving most to the people he liked rather than those he disliked. Fancy that!
Third, the country was practically bankrupt. The long war with France which was so much part of the package of Edward III's allegedly glorious reign had resulted in the crown amassing intolerable debts. The normal revenue of England was only just enough to keep things ticking over - war meant taxation, and taxation was unpopular except (rarely) when the war was going really well. It was deeply unpopular when we were losing. The appalling financial straits that Richard inherited resulted in such measures as the Poll Tax which bore down most heavily on those least able to pay. (It would seem we still have the same taxation philosophy 627 years later.)
Several historians have explored Richard's psychological profile and developed various theories the latest of which - in Nigel's Saul's biography - is that the king was narcissistic. I'm no psychiatrist but I suppose my theory is as good as anyone else's. I suspect Richard was a depressive, maybe even bipolar. This would explain the difficulty he had in functioning at times, his occasional passionate - even violent - outbursts, and the problems he had with relationships outside his 'circle of trust'.
More another day...