Here we go again...
Yes, crosstraining is beneficial to all martial artists.
Yes, grappling skills are an important addition to the training regimen of any martial artist who wants to be well rounded in terms of both fighting and self-defense.
But, no, the fact that cross-training and grappling are beneficial does not negate the fact that TMA still have a lot to offer in terms of fighting skills (i.e. striking) if trained in the right manner (i.e. alive, vs. resisting opponents).
I train in TMA. I have cross-trained in other things. I have been taken down and submitted, but I have also made grapplers eat my right cross/side kick/front kick etc.
It is the fighter and how the fighter trains, not the style, that is most important.
Sheesh, how many times do we have to say that!!!