This question seems a bit loaded - you say the US has bases in other 'nominally sovereign' nations. However, did you know that those bases are actually done with agreements by the host nation? For instance, Soto Cano Air Base in Honduras is a Honduran air base that the US leases part of it for use.

Likewise, with Korea in the news, it should be noted that South Korea actually pays a portion of the US costs of forces in Korea. South Korea very much has a choice as to whether to pay and they choose to.

To answer your question more specifically though - yes, plenty of other nations did and still maintain bases in other nations. The British Empire had bases all over the world to support its empire - from Aden in Yemen to Singapore. Heck, the UK just opened a new base recently, HMS Juffair in Bahrain.