Why are most popular songs, as heard on the radio or a streaming service, approximately three minutes long?

You could argue that it's because the early records were only able to fit about 2-4 minutes on them for "singles" which musical artists and studios would send to radio stations for play.

I find it interesting that in 1958 the Eurovision song contest limited all songs to 3 minutes, so it may just be arbitrary and expected after the technology caught up that hit songs last ~3 minutes. In fact, the vox article mentions that anything significantly longer than 3 minutes usually just gets a "radio edit" and that's because songs too long cut into profits either of the radio station (can't run ads if the song is running), or the record label ( music royalties aren't based on song length, just plays).

https://en.wikipedia.org/wiki/Three-minute_pop_song

https://www.vox.com/2014/8/18/6003271/why-are-songs-3-minutes-long

The reason dates back to early recording medium.

In 1901 a method of mass production called "Gold Moulding" was introduced by Edison. This process used a vacuum deposition of gold powder over the original recorded cylinder, followed by electroplating with copper to create a sub-master cylinder mold from which multiple copies could be made. Prior to this, performers were recorded numerous times, and multiple recorders were used to record performances simultaneously on multiple cylinders. This is a fascinating fact to consider when deciding upon preservation priorities. Considering this, there could be multiple unique performances sold! Blue Amberol cylinders made of cellulose nitrate were introduced by Edison in 1912, doubling the maximum length of the cylinder recordings to 4 minutes long. This harder material allowed for finer grooves, and therefore more information storage. Cellulose nitrate cylinders from various companies are also found in purple, pink, brown and black colors.

One competitor of Edison was the Indestructible Phonograph Co. of Albany, New York. They made molded celluloid cylinders beginning in 1907. These cylinders, sometimes labelled for Columbia, or called Oxford Indestructible have a cardboard core with metal rings at the inner ends. This was to provide physical stability.

The standard cylinders were most commonly either 2 minutes or 4 minutes in length. As with discs, the finer the groove the more information is stored, and the slower the speed of rotation for proper playback. Although speeds can vary across the duration of a single recording due to inconsistencies, especially with home recordings. Each cylinder holds a single speech, spoken performance, song, or instrumental tune. Considering the time limit, it seems a likely reason that most popular songs recorded for the radio are still typically 4 minutes or shorter!

https://www.hagley.org/librarynews/earliest-sound-recordings-short-history-cylinders