Kaleb R. answered 04/18/23
Music Theory Tutor Currently Teaching at Undergraduate Level
Thank you for your question! The beats in music can be used to either subvert or confirm our expectations. Having a reliable beat structure is very important to have a successful pop song, because most audience members do not want to listen to unpredictable music. This is why music in 4/4 or 3/4 is so popular. They are easy to feel and are very reliable for songwriters as a tool for organizing musical ideas. Audiences don't mind an occasional trick to throw off the pattern, but this should be done sparingly and not in an extreme manner. Additionally, when a measure of music reaches a point that could be broken into 3 or 4 beats like in 7/4, the measure will typically be broken into smaller units (like 1 measure 4/4 and 1 measure 3/4). It is possible to have higher counts of "beats" in the measure, but often times this describes a subdivision of the actual beat (like 6/8 is really 2 beats with a 3 note subdivision).
This is the most likely place you might find a measure of 11 or 13 is in a classical style composition. In my time as a composer, I have found that musicians prefer to see smaller units of measures. In a composition of mine from 2019, I had marked a measure of 11/8. The musicians did not like this and asked me to break the measure into two measures (3/4 and 5/8) so that they could feel the music better. I imagine this is what stops it from appearing frequently in classical style music. There are examples, such as the measure of straight quarter notes in Stravinsky's Rite of Spring. So in summary, the majority of people like music that is easy to count having reliable beat organization and musicians prefer to see smaller units of music. Together, this is why music overall does not feature beat patterns of 11 or 13.