(Parts of this answer were posted before the OP edited the question to exclude some of it - in particular,
e.g. to move up half step and
Don't discuss other music such as jazz. were added after this answer was posted.)
Has pop music ever modulated at all?!
Your terminology is rather imprecise: You seem to be drawing a hard line between Bach/Classical and everything else, which you refer to as "Pop". But what's not classical isn't necessarily "pop", which refers to a very particular genre. Rock, Jazz, Folk/World Music, various forms of "Art Music" are not classical, but they are by no means "Pop", and some of those genres make ample use of modulation. @topomorto in his excellent answer cites a great Paul Simon song, but that song is difficult to categorize as "pop" - it's a unique form of art music from a very talented and individualistic singer/song writer. AFAIK, that song was not a popular hit - it's a difficult song to perform well, and 'you can't dance to it'.
So your question is unclear, and perhaps a bit unfair as well: To divide music in the manner you have is IMO rather demeaning to every sort of music that doesn't meet your standard, which sounds like: JS Bach vs Everything Else!
I'll try to stick close to what is commonly referred to as "pop", which means music that tends to be commercially oriented, and strives to be "popular" with a broad range of "regular people", who are not necessarily musically sophisticated or literate.
A very popular technique is to move the key up in half steps (other appropriate intervals can also be used but half steps seem to be the most common) through a song to build excitement. Such devices are also common for the last verse of a pop song.
It's not a sudden key shift to a bridge part, but a gradual, controlled and contrived form of modulation in pop - hardly brutal - the band usually does play a transitional phrase or two - although not really much in the way of harmonic sophistication either:
Moves up half a step for the final refrain/fadeout - huge hit for Wilson Pickett, one of the greatest soul singers ever: (Perhaps this does fall into the category of sudden/brutal by your criteria, although the transition is quite smooth - not at all disruptive.)
Not sure if you're including jazz or not - jazz is by no means "Pop" - obviously jazz and jazz-rock (Steely Dan for example) have plenty. Here's a very famous recording, featuring modulation and the now ubiquitous Coltrane Changes:
In jazz harmony, the Coltrane changes (Coltrane Matrix or cycle, also
known as chromatic third relations and multi-tonic changes) are a
harmonic progression variation using substitute chords over common
jazz chord progressions. These substitution patterns were first
demonstrated by jazz musician John Coltrane on the albums Bags & Trane
(on the track "Three Little Words") and Cannonball Adderley Quintet in
Chicago (on "Limehouse Blues"). Coltrane continued his explorations on
the 1960 album Giant Steps, and expanded upon the substitution cycle
in his compositions "Giant Steps" and "Countdown", the latter of which
is a reharmonized version of Eddie Vinson's "Tune Up". The Coltrane
changes are a standard advanced harmonic substitution used in jazz
The changes serve as a pattern of chord substitutions for the ii–V–I
progression (supertonic–dominant–tonic) and are noted for the tonally unusual root movement by
major thirds (either up or down) by a major third interval as opposed
to more typical minor or major second intervals, see steps and skips,
thus "Giant Steps", creating an augmented triad.
Now that we've gotten to jazz, we can find the best examples of sophisticated modulation in pop music coming from Steely Dan - a revolutionary jazz/rock group (essentially comprised of Walter Becker and Donald Fagen) who have recorded music that makes ample use of modulation in modern jazz fashion. This song was discussed here:
See: Recognizing modulation style / pattern in Steely Dan's "West of Hollywood"
Steely Dan was a "pop" band in the strictest sense and they had no qualms about being referred to as such - they enjoyed making popular music and they said so. They were a huge commercial success with a number of Top 40 hits - and they made ample use of modulation in many, if not all of them: Count the key changes in these songs:
Why pop music rarely modulates?
- It's not necessary, in fact it's often detrimental : Pop music is
designed to be Popular: Pop artists want to make music that
ordinary people can easily relate to - it should be pleasing and
catchy so people can easily connect with it, sing along with it,
relax with it, dance to it, etc. Sophisticated modulation along the
lines you are speaking of doesn't do much for any of that - just makes
it more difficult. How can you hum along with a song that keeps
modulating through the circle of 5ths?
- Many pop artists don't have the formal training required to make the
sort of sophisticated music you're talking about.
What is the difference between the chord sequence of pop music and
J.S.Bach that makes the former modulates less?
Not sure this part of your question makes much sense: Nothing "makes" it modulate less, musically speaking. Pop music simply doesn't generally use such techniques, as explained. A pop artist who was well educated musically and wanted to use modulation could certainly use it, however if there was more than a very moderate amount, it would no longer be pop, but some form of "art music".
In a very broad sense, we could say that the more technically sophisticated and complex music tends to be, the further it strays from the "Pop" genre, by definition, as explained. Technically speaking, there is no reason why the Beatles "I Want Hold Your Hand" could not be played with Coltrane Changes, or any other sort of modulation, but what purpose would that serve? It would ruin the song!
Has pop music ever modulated at all?!
Steely Dan's music shows indisputably that sophisticated, elegant modulation is used very successfully in "pop" music, even using the narrowest definition of that term. There are plenty of other examples as well, but AFAIK, none have done it was well, or had as much commercial-"pop" success as Steely Dan. IMO they were "a cut above".
Having said that, I'll stand by my contention that more often that not, complexity tends to denigrate the "popular" value of "pop", at least by the standards the post WW II, rapid/mass communication/hi-tech period. Pop music does not need modulation to be "good" or successful, any more than Bach needs a good lead guitarist.