Grabbing the line is actually quite common when fishing with a tenkara rod. Although most people use a line about the length of the rod, to which they'll add 3-4' of tippet, some use longer lines. The longer lines tend to be the 1.5 times rod length that was also used with the English loop rods 150-200 years ago.

Even with a line the length of the rod (not counting the extra 3-4' of tippet), you will have to hand line the last few feet unless the fish is quite small. The rod bends so much, particularly with a large fish, that you cannot possibly net it otherwise.

As in everything else, there is a trick to it. It has to be done in one motion that is smooth enough and quick enough that the fish cannot turn it's head to start another run. If it manages to do that you have to immediately let go of the line and start again, timing it for when you can get the fish coming directly towards you by angling the rod back over your shoulder.

You absolutely do not have to tire a fish to exhaustion to do that. My best fish on a tenkara rod was an 18 3/4" wild brown that was in the net in less than a minute from the strike.