Rebound is not inherently good. It's just what happens. Controlling it is not a bad thing, IMO, because it can lessen head injuries from slamming into the back of the seat. There are other ways to achieve it than with a RF tether (anti-rebound bar; seat handle left up on bucket seat that allows it.) I personally feel it's a good idea. With this particular type of rebound control, the RF tether, yes, it adds a bit of strain to the neck. Some people feel this is too much for a newborn. I tethered my newborn from birth without hesitation but some won't for that reason. Some opt to leave a seat untethered, or to get one with an anti-rebound bar or an infant seat and leave the handle up, instead. Most people have no qualms about doing it with an older, stronger child.
Britax says to just remove slack, not change the angle of the install. They had problems with recline mechanisms being broken by overtightening.
Sunshine Kids, the only other brand that allows RF tethering, allows you to change the angle-- there's not a recline mechanism to break on that seat. You definitely can overrecline in some cars if you tighten enough to pull it back too far.
Personally, I think rebound control is a Very Good Thing. But the decision on whether to tether or not is up to you, the parent. If you feel otherwise, by all means, don't tether. It's not required.