Regarding the other variants of AES-GCM
-TLS_RSA_WITH_AES_128_GCM_SHA256
There are some sites support AES-GCM that use only ciphers with RSA key 
exchange. I think it would be best not to support new standards that 
don't provide Forward Secrecy, but on the other hand, if this cipher is 
enabled then users browsing to those sites will at least have something better 
than RSA with AES-CBC. If I'm correct, AES-GCM is not vulnerable to some of the 
newer TLS attacks, in particular Lucky13. Even when used together with TLS 1.2, 
AES-CBC is 
vulnerable to Lucky13.
-TLS_DHE_RSA_WITH_AES_128_GCM_SHA256
I'm
 aware that a lot of sites only use 1024 bit DH, but with the patent 
issues regarding ECC, there are still enough sites who don't support 
ECDHE. If this cipher is enabled, users can benefit both from protection
 against Lucky13 and Forward Secrecy. Also there are enough sites out 
there that do have 2048 or even 4096 bit DH key exchange. 
For sites 
that have both ECDHE and DHE ciphers enabled, ECDHE variants are usually
 the preferred anyway and if the server has no preference, they are also
 preferred by NSS. I also think that diversity should be maintained in 
case a vulnerability in some standard or protocol is discovered. Just 
like supporting ChaCha20_Poly1305 and AES with other modes like CCM to avoid 
the same 
disaster as with the BEAST attack, where AES-CBC was the only really 
secure protocol, found vulnerable and then having tons of sites switch 
back to the insecure RC4. Just in case ECC is being discovered 
vulnerable, there should be an alternative key exchange method that does not 
use EC cryptography. The only widely used are RSA and DHE, and DHE 
supports Forward Secrecy and is the better alternative IMO.  
Bruce Schneier believes ECC is relatively easier to break for the NSA. Whether 
or not you find his advice important, the fact is that ECC is 
relatively new and there should at least be one older and proven method as well.

As
 discussed before, ECC cryptography has better performance, but if 
webmasters prefer performance then they put DHE ciphers lower in the 
order  or disable them completely. IMO, the weighing whether to prefer 
performance or security is the choice of siteowners and webmasters. By 
supporting only variants you or someone else prefers, you're limiting 
their choice.
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