You can think about music as tones.  Tones have pitch (higher/lower) and texture (hard, soft, rounded, pinched...you name it).  Each instrument has a tonal range--it can't play every possible pitch (think of the topmost note on a cello--violins play higher; vice versa, the lowest note on a violin is higher than the lowest note on a cello.)  The composition of an instrument (wood, metal, plastic, mixes of materials) and its shape (solid, hollowed out in one, two, three sections etc.) gives it a specific texture (the difference between the sound of an un-plugged-in electric guitar [solid body] and an acoustic guitar [hollowed out body]...

Percussion instruments have tones--tubular bells are pitched, as are gongs, timpani, triangles, even a snare drum has a specific range of tones--the thinner the snare the higher the tone....

From tones you can create melodies--sequences of tones--and harmonies--more than one tone playing at the same time.

Counterpoint (Bach!) is music for two (or more!) melodies--but staying with two, you have two different sets of notes being played.  Imagine one person whistling one tune while another person whistles a different tune.  Where the two tunes overlap, you get harmonies--Bach is the master of this mix of harmony and melody just using (but not only!) a maximum of only two notes at a time, and often just one.

Here's some music (breaking the page!): you can see three notes being played together at the beginning, then on the top line a series of notes; on the bottom line a different series of notes.

You can see the bar lines too (the vertical black lines--the first one appears after the fifth note at the top moving left to right.)

At the very left you can see a 3 above a 4.  Ignore the 4 and think of the three: it means there are going to be three beats in every bar.  If you look at the top line in the second bar, you can see the three beats.

It doesn't matter which instrumentare playing: they all have to play beats.

That's not true, though.  A trumpet can appear softly, grow louder, then fade, and this effect may appear outside of the basic ONE two three structure.  Percussive instruments are those that automatically play a beat (think of hitting something--a definite pulse; think of slowly breathing out--it has a beginning, but no clear pulse--though rising and falling are what pulses do...among other things!)

If you want people to dance a waltz you play three beats with the emphasis on the first beat.  ONE two three, ONE two three, ONE two three, ONE two three--and everyone starts dancing.  Note that there are four "ONE two three" groups: That's a round, your brain feels a "coming back to the beginning".

Now-let's get strange.  Let's call that a FOUR beat.  Each beat is broken into three parts, so imagine saying

ONE two three four
ONE two three four
ONE (two three) two (two three) three (two three) four (two three)

If you feel a pulse, that's rhythm.  If you enjoy the pulse, if you enjoy the movement, your body moves.  If the music goes POOM!  POOM!  POOM! POOM! it's playing a fourbeat, and each beat is a single POOM!  If you imagine POOM! POOM! POOM! POOM! you can imagine nodding your head to it...but not to ONE (two three) two (two three.)

Rock music is four beat, with two emphasis points: one the first beat and the third--

u-ONE two Three four.  Normally the Bumfh! first beat is played with a bass drum, while the tink! third beat is played on a higher sounding instrument, such as a snare drum.  The second and fourth beats are usually tapped out on a cymbal of some kind.  (boom an chich an, boom an chich an....four beats)

So anything can become a fourbeat: you take whatever crazy pattern you like and repeat it four times.  Each repetition of the crazy pattern is a beat.  The simplest pattern is BOOM! or TING! or HUH! or Yeah!...

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Historically, humans have found many other patterns than the circular four.  The circular four is good for trance-states (similar to the no-beats in ambient music--only the four beat is more--active!  more energetic.  Anything that isn't playing fours sounds cerebral--you have to think about it; but not if from birth you have consistently heard various beat patterns and also observed specific movements enacted to the various patterns.  Some music doesn't have an overall beat.  It gets faster, changes patterns when maybe a dancer acts out a different character.

I think rhythmic diversity--the pleasure in the various different patterns and patterns of patterns we can create--is energising.  I understand "dumbing down" as the process whereby a new generation can no longer appreciate a rhythm different to POOM! POOM! POOM! POOM! or maybe an UmpaChinkaUmpaChinka.  That's unfair, though, as much fourbeat music has great variety inside each beat--trouble is, then they loop it up and it stays the same for the whole song!  But maybe that's okay if the melodies and harmonies are supposed to be at the forefront.  There are crazy tunes that burst out--you hear one and mention it to another person who says, "Yeah, I know it, it's lovely!"  or banging or the top or top rate or really rather good--ya know, it gets an affirmation as music.

Part of european tradition has been to write music down as notes so that another player at another time can make the same music--note perfect--and with the correct rhythm: that 3 back there that said there are three beats to a bar, so the music will go ONE two three ONE two three--only of course it doesn't, because melodies may be stretched across bars so that the rhythm becomes ONE and two and three AND one AND two AND three AND ONE and two and three and....

Drummers learn to play the beats on their instruments--and as their instruments have a percussive sound--BUMF! WHOOMF! Crash boom tink shk po ta--the rhythmic qualities are clearly present.  The same goes for a piano, which is a percussion instrument with a large tonal range, so it can play rhythms at the same time as melodies and harmonies.

Because we all enjoy fourbeat rhythms, because we enjoy the circularity, but are also prone to boredom, any instrument can use the internal beats to create alternative rhythms within the individual beats

ONE (two three) two (two three) three (two three) four (two three)

(a) ONE (anna) two (a give me a) three (hey hey boy) four (!) anna ONE...

So your question:

Don't they have a whole variety of beats to get used to?

The answer is yes--but change "beats" to rhythms and note that so does every musician, meaning every person directly involved in playing a specific piece of music.

Heh!  You got me rambling.  I hope that's of some use!

Don't fight forces, use them R. Buckminster Fuller.