I wish suppressors (we really have to stop calling them silencers) had been legal and available when I was learning to shoot, and doing target shooting. Like a lot of people, my brain didn't really develop until I hit my forties or so (my wife would argue with that), by which time I had (and have) permanent ringing in my ears.
Apart from the myths created and perpetuated by Hollywood, it's difficult to see the downside of suppressors.
Suppressors don't eliminate noise. On a supersonic round (most rifles), they take the 'crack' out of the shot, which takes away the pain of shooting without ear protection, but doesn't eliminate it. The sound is still loud by any reasonable definition. On subsonic rounds fired from semi-autos, they reduce the noise but again, not so much that you could shoot squirrels in your backyard and not have a SWAT team at your doorstep. With revolvers I don't think they have much effect at all.
While there are no downsides I can see, there are upsides.
Firstly, for the Hollywood crowd, a handgun fitted with a suppressor is far harder to conceal than one without. If you carry it in the front, people may think you've just met Mae West.
Secondly, they are less disruptive to the animals (other than the one being shot, of course!) and anyone else who might be within hearing distance of the shot, such as farmers and ranchers. Makes for a nicer weekend.
Thirdly, they do reduce recoil - I've seen the video, but I also have the evidence of my senses. I used a .300 win mag and a .25-06 last summer on a cull hunt in South Africa. As much as I love my .300, I'm not prepared to put 40 rounds through it in the course of about 5 hours. Not only would it hurt like hell, but I'd likely develop a flinch of the worst kind.
Fourthly, as noted above, it's a health issue for the hunter and those around the hunter.
I said there were no downsides. There is one. They are a bit ugly. They would unbalance my beautiful rifles, and they would require that I thread the barrels. So I'd use them when I was target shooting (without my hunting guns) and when culling (when I use someone else's gun!).