You don't necessarily need root tabs but it will definitely help them grow! My swords were fine without them but they started to get flimsy so I added root tabs and now they're much healthier, growing quicker and firmer leaves.
Yeah I don't think that's very true about the hairgrass....I've seen plenty of youtube vids were people are cutting their carpet's because well...it grows!! lol Although if you are worried about it, don't trim the top, give the roots a bit of a trim and then plant it. For the first month or so it's not going to do much but once it's fully acclimated to the water chemistry and the lighting, it will start to grow and then you can trim after that ^_^
Leopards: 1:4 Hawkeye, Luna, Astrael, Dorian, Cullen