I am quite new at nonstandard analysis, and recently I became aware of its use in probability theory mainly through the following two books:

• Nelson (1987). Radically Elementary Probability Theory
• Geyer (2007). Radically Elementary Probability and Statistics

Although Nelson's book is several decades old, as far as I can see, its approach has not yet caught on. Also, I couldn't find a lot of papers published in the leading probability journals on that topic. I am quite intrigued by that phenomenon. My questions are the following

• Why hasn't nonstandard analysis been widely adopted by probabilists?
• Were there some success stories in some particular sub-fields of probability theory or statistics?
• Does there exist some known fundamental objections in probability theory to the approach in there?