Now this is getting out of control.  I mean the drum rings are one thing but muting cymbals is another.  No matter what you do the sound of the cymbal will change the moment anything touches it no matter how light.  There is no way around it.  The edge of a cymbal vibrates in a huge manner. 
 
The problem are the drummers themselves.  They are simply hitting cymbals way too hard.  The thing is a cymbal can produce a lot of sound with only a very light stroke.
 
It is better to master the concept of the amount of power you use on a cymbals.  It is hard because some drums need to be hit harder (toms usually) and others not so hard and cymbals a different level of power again in order to get a very even level over all the drum surfaces.  That takes skill.  Experienced drummers can do it and it sounds much better.  I can do it but I have learned from years of recording myself  (a single mic ohead as well nothing fancy here) and hearing back how things sound.  Over time I have adjusted the amount of power required for the surfaces in order to get the perfect drum sound.  That is the way to learn how to do it.
 
Another problem area is the snare.  Most drummers hit it way too hard as well.  The snare drum can produce a very clear audible level even when you let the end of a stick drop under its own steam/gravity to the surface.

I laugh at most drummers cause they seem to think it's a contest to see who can hit them the hardest.  I have used e-drums for years, and drummers that use them don't like them because they hit them so hard they don't like the noise if they don't have a monitor over their head.  Idiots... I get the same sound on them with light touch and lightweight sticks... and the bounce is better that real acoustics so you can move faster... of course I don't have the strength I used to.  I can't listen to small venues with banging drummers because they fill the space with too much noise and the rest of the band can't manage their sound over the drums.

When you compare drums to most other acoustic instruments they are actually quite a bit louder.  So what drummers should be doing is dropping the amount of sound they make from the drums to match everything else.  (instead of the other way around) Even when playing through a big PA when you do that it works well.  Lovely even stage volume from everyone and a big loud sound out front.
 
Being a recording engineer helps though because I have always adjusted my volume on stage so that I was hearing a perfect well balanced mix.  Once you drop the drum levels down everything else just sounds amazing and very nice and seems to fall into place.  No one has to work over hard either.  The audience and the venue will love you forever!  They also record beautifully when hit way less hard too.  You get a horrible thin sound when you smash them.  When you play them at the right level they sing and sound fat.
 
With regard to cymbals I use to play in an Orbison/Presley tribute band.  There was a lot going on and we had a lovely lowish stage volume but a big sound out front.  I used to worry sometimes when the sound guy did not put mics on the hats or overheads.  All I had to do was use nylon tipped sticks and he said he could hear my hats and cymbals right over the top of the herd of elephants that was coming out front.  Isn't that interesting and I was not even hitting the cymbals hard at all, just playing the ride and hats at normal to low levels and crashing gently.  He used to say to me that if he miked them up they would end up too loud!

In the one lesson I ever had, from the house drummer of the Bird Cage in London, when I started playing drums was do not hit cymbals straight on, hit with glancing blow, gives much more control over volume, timber etc.

This drummer shows how it should be done:
 
https://www.youtube.com/watch?v=L5CgdTtGv8o
 
Notice he ain't banging the crap out of them.
 
Dan

I used to play in a band where the drummer was LOUD.... seriously loud.  We were playing at around 118dB... yeah crazy loud.... and when the drummer took his solo, it went to 121dB on stage.... and he was miked...
 
He'd buy a new cymbal and in a few weeks it would be cracked. He didn't have any cymbals that weren't drilled in an attempt to stop the cracks... One night, he hit his crash and the crack instantly ran completely around the cymbal and the outter 2" fell down the stand.... and he had a new splash cymbal.

That band was fun, and we played a lot, but it ruined my high end hearing. We were young, stupid and loud.

dcumpian
This drummer shows how it should be done:
https://www.youtube.com/watch?v=L5CgdTtGv8o
Notice he ain't banging the crap out of them.

Yes great example.  This is at the top end of hitting the drums but as you say still not smashing them.  Notice how he gets a nice sense of pushing and energy without all the smashing.  So many drummers think the energy is related to the level of hardness and loudness you are hitting the drums but in a way it has nothing to do with it.  It is all about driving the beat and placing the hits in the right place musically, timing wise. 
 
One of my drum teachers used to say let the energy flow right down your arm but stop it at the wrists and just let enough through to do the job.
 
Also notice how nice the snare sounds in this video.  Even though it is close miked it still sounds good and fat. He is not pounding the snare at all.  This is about as hard as I would get in force and loudness.  There is still plenty of dynamic range below this level too.
 
Herb if you are breaking sticks, heads and destroying cymbals or bleeding you are doing something wrong.  I have never broken a stick, head or cymbal in 46 years of playing.  End of story.
 
In terms of volume the whole band should be aiming for about 105 dB SPL which is known to be the most exciting sound pressure level.  (What a symphony orchestra can only reach in full force acoustically)  Anything over is bad and it all starts to go downhill from there.
 

You guys are all so spot on! The problem is...while drummers are learning to play, they are not focusing on dynamics or what I like to call "finesse drumming". This takes time. Sort of like guitar players that go for all the mean licks and cool scales etc. They don't come into their own and learn actual "melodic phrasing" until they have played quite a few years.
 
Until drummers can get that finesse quality, we have to use baffle boards (plexi-glass) and cymbal tamers. My drummer hits rather hard, but is also quite a finesse guy. He can turn it off and on which is cool. Us being a rock band, well, most of the stuff sounds better when he really hits it. That said, it forces us to have to turn up and that is one thing I have always been against. The louder you are on stage, the harder it is for your singer, the worse it is for your audience hearing all that raw sound coming off the stage.
 
What we do in situations like that....our drummer uses those Rodz things. You know, the sticks that look like 50 long stick matches that light your grill/stove were banded together? It's amazing how much this cuts down on the drum volume and allows the drummer to still beat the heck out of the drums. It not only saves heads and voices from screaming....it saves your ears.
 
Also, I have noticed quite a bit more ring in some of the cymbal selection drummers are bringing into my studio. Some of these things don't really sound that good to be honest. They last forever after you hit them, and the quality is not veryt good. Some of the Sabian stuff just annoys me, but it seems to be one of the weapons of choice from quite a lot of players. I've literally had to strategically tape or even put putty on cymbals that annoyed me or sounded bad. Sometimes you can't eq them to sound right because they are just a poor quality cymbal....or maybe all the drummer could afford. You learn to handle things as they come your way. Sometimes it's a challenge, other times you catch a break. :)
 
-Danny