On Burma (Myanmar) not sure this the depth of answer you want (or of the level of professional historian which the mods will approve of) but the section of Burma containing the Shwedagon Pagoda, Rangoon (Yangon) wasn't occupied until the 19th century (1852) after the second Anglo-Burmese war.

Until then it was protected by a series of Burmese Kings/rulers with armies of reasonable size and a local population of more than reasonable devotion. In other words it's not an easy thing to pillage.

Some Europeans did succeed in attacking Burma and looting objects from the Shwedagon and other Pagodas before the British occupation. Notably the Portuguese mercenary, Filipe de Brito who stole and then lost the great bell of Dhamezedi in the Bago river as he tried to ferry it away.

Important to consider is also the nature of what we see now as the Shwedagon Pagoda and it's historic state. Currently is does have a lot of gold on it, but this has not always been the case. Constant repair, upkeep and improvements to the Pagoda have changed the amount of gold on and around the structure. To understand the fluid nature of the state of the Pagoda you only have to see the proliferation of flashing neon lights around the statues in shrines at its base, or escalators and lifts taking people up and down the Singuttara hill.

In other words, yes it's big and covered in gold, but much of that is gold leaf (or even paint) and the actual amount of gold in or on the structure may not be as much as it appears and has varied over time. What we see now is not how it has always been and the pagoda is by no means and has never been solid gold.

Consider that the main thing of note de Brito chose to steal was a brass bell from Shwedagon, not gold. Because brass had a value in being turned into cannons yes, but also because scraping gold leaf off of a Pagoda isn't going to make you much money, especially when the locals aren't to happy about it.

After lower Burma was occupied in the 19th century looting of pagodas did occur, but although looting happened is was mainly of more portable smaller gold statues as well as other gold and gems. Interestingly Shwedagon at the time sat above the main city of Rangoon and was considered a strategic site by the British and so became a gun emplacement, with no access to the locals.

The main criticism of the British in their occupation by Burmese at the time was not that they were stealing all the gold, but rather that they refused to take their shoes off when in the Pagoda precinct and wouldn't let local Burmese into the site.