It's actually pretty simple, he never had a powerbase within Germany to enforce his rule and negotiate with the Pope.

So some background. While the Imperial title was tied to the elected king of Germany, it still primarily followed dynastic lines. And the Emperor was one weight in the balance of power, along with the collective nobility of the empire i.e. the "Princes of the Empire," and with the papacy.

The entire existence of the Hohenstaufen dynasty was bound by conflict with the Papacy, with key German nobles throwing their weight towards each party as they believed would benefit themselves. The Emperor, when they need security within the Empire from other nobles, and with the pope/anti-kings when the Emperor was getting too powerful for comfort.

This brings us to the last Hohenstaufen emperor, Frederick II. Who was King of Sicily, king of Italy, Emperor and a host of other titles. The pope, Innocent IV, was able to successfully excommunicate Frederick and dethrone him in Germany.

This is the start if the long list of Anti-Kings. First was Henry of Thuringia who was elected and backed by the pope and some nobles while Frederick was still Emperor. However Henry died in a few months.

Then William of Holland was picked as anti-king but gained acceptance after Frederick's death. He ruled for 8 years but never secured his own rule in that time; it was pretty common for a few years to pass between being crowned king and being crowned emperor.

Here Richard gets another contested election with his connection to the Plantagenets and therefore the Welfs, notably Otto IV Emperor.

He was challenged by Alfonso of Castile. He was the grandson of Philip of Swabia King of Germany, son of Frederick Barbarossa. The old imperial party wanting to restore the Hohenstaufen line, with Hohenstaufen heirs being hunted down across Europe.

Now Alfonso and Richard had zero powers within Germany. Richard being closer was able to actually make it to Germany and married a German bride but otherwise couldn't do much.

Alfonso eventually gave up his own claims and that allowed Richard to become "uncontested" as king, but neither Pope or Princes had any interest in a return of an Emperor.

Richard had a son named Edmund but Edmund nor any Welf party supported his own claim to the Kingship. It's not a way to get rich quick.

Rudolf Habsburg, a Swabian count turned dual duke of Austria & Styria had built up a powerbase with southern Germany and with that was able to defeat the Bohemian King Ottokar in battle and secure the kingship for himself.

Rudolf and the following "count-kings" spent their reigns working to restore royal authority north of the alps and would not make serious efforts to go to Rome; which was always a money sink for men and resources, and many previous Kings had traded away imperial powers to the popes for recognition of their legitimacy.

I'm going to skip ahead a little and arrive at Henry of Luxembourg, who was able to secure the election as King and use his friendship with the French King Philip the Fair to gain the recognition of Pope Clement V, the first Avignon Pope.

So gaining the imperial coronation for Henry was relatively easy however, he also had limited powerbase within Germany and his dynasty's rule would continue to bounce back and forth with the Habsburgs until Frederick III secured the imperial coronation and the Habsburg dynasty remained (mostly) unchallenged until 1806.

So just going back to the question why Richard wasn't ever crowned Emperor? Despite that damned Voltaire quote that I hate so much and the usual short hand that "the HRE was more like a confederacy" The King of Germany needed real 'on the ground' power to enforce his rule, gain the imperial coronation, and actually govern within the Empire.

Richard had no power within Germany nor leverage with the pope to be crowned.

I asked a similar question that /u/WelfontheShelf gave a great answer to.